{"id":234,"date":"2023-07-10T19:00:18","date_gmt":"2023-07-10T19:00:18","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%9c%86%e5%91%a8%e6%96%b9%e7%a8%8b-%e6%99%ae%e9%80%9a%e5%85%ac%e5%bc%8f-%e4%b8%80%e8%88%ac%e4%be%8b%e5%ad%90-%e5%b7%b2%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T19:00:18","modified_gmt":"2023-07-10T19:00:18","slug":"%e5%9c%86%e5%91%a8%e6%96%b9%e7%a8%8b-%e6%99%ae%e9%80%9a%e5%85%ac%e5%bc%8f-%e4%b8%80%e8%88%ac%e4%be%8b%e5%ad%90-%e5%b7%b2%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%9c%86%e5%91%a8%e6%96%b9%e7%a8%8b-%e6%99%ae%e9%80%9a%e5%85%ac%e5%bc%8f-%e4%b8%80%e8%88%ac%e4%be%8b%e5%ad%90-%e5%b7%b2%e8%a7%a3%e7%ad%94%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u5468\u957f\u65b9\u7a0b"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5706\u5468\u65b9\u7a0b\u7684\u6240\u6709\u5185\u5bb9\uff1a\u666e\u901a\u65b9\u7a0b\u3001\u4e00\u822c\u65b9\u7a0b\u3001\u5176\u4ed6\u7c7b\u578b\u7684\u5706\u5468\u65b9\u7a0b\u3001\u4f55\u65f6\u5706\u5468\u65b9\u7a0b\u6b63\u786e\u2026\u2026\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u770b\u5230\u5982\u4f55\u627e\u5230\u65b9\u7a0b\u7684\u793a\u4f8b\u5706\u5468\uff0c\u60a8\u53ef\u4ee5\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-ordinaria-de-la-circunferencia\"><\/span>\u666e\u901a\u5706\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u4e86\u89e3\u4ec0\u4e48\u662f\u5468\u957f\u65b9\u7a0b\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u56de\u987e\u4e00\u4e0b\u5468\u957f\u7684\u6982\u5ff5\uff1a<\/p>\n<p>\u5706\u5468\u662f\u5e73\u9762\u4e0a\u4e0e\u79f0\u4e3a\u4e2d\u5fc3\u7684\u56fa\u5b9a\u70b9\u7b49\u8ddd\u7684\u70b9\u7684\u8f68\u8ff9\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-de-circonference-1.webp\" alt=\"\u5706\u7684\u65b9\u7a0b\u662f\u4ec0\u4e48\" class=\"wp-image-1991\" width=\"288\" height=\"273\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u5706\u4e0a\u7684\u6240\u6709\u70b9\u5230\u5706\u5fc3\u7684\u8ddd\u79bb\u90fd\u76f8\u540c\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5706\u662f\u4e0e\u692d\u5706\u3001\u629b\u7269\u7ebf\u548c\u53cc\u66f2\u7ebf\u4e00\u8d77\u7684\u56db\u4e2a\u5706\u9525\u66f2\u7ebf\u4e4b\u4e00\u3002\u5373\u7528\u5e73\u884c\u4e8e\u5e95\u9762\u7684\u5e73\u9762\u5207\u5272\u5706\u9525\u4f53\u5373\u53ef\u5f97\u5230\u5706\u3002<\/p>\n<p>\u5728\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u63cf\u8ff0\u5706\u7684\u6700\u7b80\u5355\u65b9\u6cd5\u662f\u6839\u636e\u5176\u666e\u901a\u65b9\u7a0b\u3002\u56e0\u6b64\uff0c\u5468\u957f\u5e38\u65b9\u7a0b\u7684\u516c\u5f0f\u5982\u4e0b\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"><strong>\u5706\u7684\u666e\u901a\u65b9\u7a0b<\/strong>\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px\">\u91d1\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5706\u7684\u534a\u5f84\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5706\u5fc3\u7684\u5750\u6807\uff1a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f5efef3ea46a765419553313f5ca6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<p>\u867d\u7136\u6211\u4eec\u4e0d\u4f1a\u6f14\u793a\u5b83\uff0c\u56e0\u4e3a\u5b83\u6709\u70b9\u4e4f\u5473\uff0c\u4f46\u8fd9\u4e2a\u65b9\u7a0b\u53ef\u4ee5\u4ece\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\u5f97\u5230\u3002<\/p>\n<p>\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5706\u7684\u5e38\u65b9\u7a0b\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1a<\/p>\n<ul>\n<li>\u6c42\u4ee5\u8be5\u70b9\u4e3a\u5706\u5fc3\u3001\u534a\u5f84\u4e3a5\u7684\u5706\u7684\u5e38\u65b9\u7a0b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61ed8ca74441b9c9ed7efef1a47bd204_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(3,-1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p>\u5706\u7684\u666e\u901a\u65b9\u7a0b\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7528\u672a\u77e5\u6570\u6765\u4ee3\u66ff<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7531\u534a\u5f84\u503c\u548c\u672a\u77e5\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5206\u522b\u7531\u5706\u5fc3\u7684 X \u548c Y \u5750\u6807\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b3bfb9b8a5a2dfb5d73ed3986567c4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-3)^2+(y-(-1))^2=5^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"211\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u5706\u7684\u666e\u901a\u65b9\u7a0b\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5847df3cfa46d4ba66d0caba4026dabe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(x-3)^2+(y+1)^2=25}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-general-de-la-circunferencia\"><\/span>\u5706\u7684\u4e00\u822c\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53e6\u4e00\u79cd\u5706\u5468\u65b9\u7a0b\u662f\u4e00\u822c\u65b9\u7a0b\uff0c\u5b9e\u9645\u4e0a\u5b83\u662f\u6700\u5e38\u7528\u7684\u3002\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u5982\u4f55\u4ece\u4efb\u4f55\u5706\u5468\u7684\u5e38\u65b9\u7a0b\u4e2d\u83b7\u5f97\u5176\u4e00\u822c\u65b9\u7a0b\u3002<\/p>\n<p>\u8003\u8651\u5706\u7684\u666e\u901a\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u5f00\u53d1\u51fa\u5353\u8d8a\u7684\u7b49\u5f0f\uff08\u6216\u5353\u8d8a\u7684\u4ea7\u54c1\uff09\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4d2b00fd17214927aa165291c8aebce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+a^2-2ax+y^2+b^2-2by=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"269\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f787480794d72c03ba5880758dedeee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-2ax+y^2-2by+a^2+b^2-r^2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5bf9\u53d8\u91cf\u8fdb\u884c 3 \u5904\u66f4\u6539\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f0414589c97ababc91d90e8b4d76f3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=-2a \\qquad B=-2b \\qquad C=a^2+b^2-r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"337\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u6700\u7ec8\u6211\u4eec\u5f97\u5230\u5706\u5468\u7684\u4e00\u822c\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8890b7cc400fafc2f805ca67e08881ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u56e0\u6b64<strong>\uff0c\u5468\u957f\u4e00\u822c\u65b9\u7a0b<\/strong>\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8890b7cc400fafc2f805ca67e08881ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5176\u4e2d\u5706\u5fc3\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e64305413efd35fdc4d0650acf78623d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(-\\frac{A}{2}, -\\frac{B}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"111\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5706\u7684\u534a\u5f84\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee6df58c142869c04d0db23bda17b0fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r=\\sqrt{\\left(\\frac{A}{2}\\right)^2 +\\left(\\frac{B}{2}\\right)^2-C}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"211\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u6240\u4ee5\u8fd9\u4e2a\u5706\u5468\u65b9\u7a0b\u603b\u662f\u7531\u666e\u901a\u65b9\u7a0b\u5f97\u5230\u3002\u4e0b\u9762\u662f\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a<\/p>\n<ul>\n<li>\u6c42\u4ee5\u8be5\u70b9\u4e3a\u5706\u5fc3\u3001\u534a\u5f84\u4e3a6\u7684\u5706\u7684\u4e00\u822c\u65b9\u7a0b\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39163542e992aade309d98d420e1a89e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(2,4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p>\u9996\u5148\u6211\u4eec\u9700\u8981\u627e\u5230\u5706\u7684\u666e\u901a\u65b9\u7a0b\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u4ed6\u7684\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b24acf89d8fb3cfb6b48d8ce985f3e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-2)^2+(y-4)^2=6^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8fdb\u884c\u64cd\u4f5c\uff0c\u76f4\u5230\u627e\u5230\u5706\u5468\u7684\u4e00\u822c\u65b9\u7a0b\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u76f4\u5230\u6211\u4eec\u65e0\u6cd5\u518d\u7b80\u5316\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68b827aa8155ab22926ac9ab1ae78745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2^2-2\\cdot x \\cdot 2+y^2+4^2-2\\cdot y \\cdot 4=36\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"324\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6651ecf7c153c784e8a0c7e01522be4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+4-4x+y^2+16-8y=36\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e0dcac8662f04c52e566c31069c1615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-4x+y^2-8y+4+16-36=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"279\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e73476ebd4ceb89a5683bcb06af09eda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-4x+y^2-8y-16=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdb5e1831804822235795e661323b911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^2+y^2-4x-8y-16=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u867d\u7136\u95ee\u9898\u6ca1\u6709\u8981\u6c42\uff0c\u4f46\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u8ba1\u7b97\u627e\u5230\u7684\u65b9\u7a0b\u7684\u5706\u5fc3\u548c\u534a\u5f84\u6765\u9a8c\u8bc1\u5b83\u662f\u5426\u6b63\u786e\u3002<\/p>\n<p>\u4e3a\u4e86\u786e\u5b9a\u5706\u7684\u4e2d\u5fc3\uff0c\u6211\u4eec\u4f7f\u7528\u5b83\u7684\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e64305413efd35fdc4d0650acf78623d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(-\\frac{A}{2}, -\\frac{B}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"111\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0eb46f8005ca0cb4418d019c01d090b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(-\\frac{-4}{2}, -\\frac{-8}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"128\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8350046e2eed3457177b5d4c040fcdcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\bigl(-(-2), -(-4)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"137\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa2b1a6a7b85d8f05bf091b50d99e060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(2,4\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5706\u5fc3\u4e0e\u58f0\u660e\u7684\u4e2d\u5fc3\u91cd\u5408\u3002<\/p>\n<p>\u6211\u4eec\u8fd8\u7528\u516c\u5f0f\u68c0\u67e5\u5706\u5468\u7684\u534a\u5f84\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-04dc99d462a8ceb5e6dca936999a4ce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} r &amp; = \\sqrt{\\left(\\frac{A}{2}\\right)^2 +\\left(\\frac{B}{2}\\right)^2-C} \\\\[2ex] &amp; =\\sqrt{\\left(\\frac{-4}{2}\\right)^2 +\\left(\\frac{-8}{2}\\right)^2-(-16)} \\\\[2ex] &amp; =\\sqrt{\\left(-2\\right)^2 +\\left(-4\\right)^2+16} \\\\[2ex] &amp;= \\sqrt{4+16+16} \\\\[2ex] &amp;= \\sqrt{36} \\\\[2ex] &amp; = 6 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"309\" width=\"260\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5e76\u4e14\u534a\u5f84\u4e5f\u7b49\u4e8e\u8bed\u53e5\u7684\u534a\u5f84\u3002\u56e0\u6b64\uff0c\u8ba1\u7b97\u51fa\u7684\u5468\u957f\u65b9\u7a0b\u662f\u6b63\u786e\u7684\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"existencia-de-una-circunferencia\"><\/span>\u5706\u5468\u7684\u5b58\u5728\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6240\u6709\u65b9\u7a0b\u7684\u5f62\u5f0f\u4e3a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8890b7cc400fafc2f805ca67e08881ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5bf9\u5e94\u4e00\u4e2a\u5706\u3002\u56e0\u6b64\uff0c\u8981\u4f7f\u6b64\u7c7b\u8868\u8fbe\u5f0f\u771f\u6b63\u6210\u4e3a\u5706\u65b9\u7a0b\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b 3 \u4e2a\u6761\u4ef6\uff1a<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u7684\u7cfb\u6570\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span>\u548c\u7684<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5b83\u4eec\u5fc5\u987b\u7b49\u4e8e 1\u3002\u8bf7\u8bb0\u4f4f\uff0c\u5982\u679c\u4e24\u4e2a\u53d8\u91cf\u524d\u9762\u90fd\u6709\u4e00\u4e2a\u4e0d\u662f 1 \u7684\u6570\u5b57\uff0c\u4f46\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u6570\u5b57\uff0c\u5219\u6574\u4e2a\u65b9\u7a0b\u53ef\u4ee5\u9664\u4ee5\u8be5\u6570\u5b57\uff0c\u4ee5\u4fbf\u5b83\u4eec\u7684\u7cfb\u6570\u4e3a 1\u3002<\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u65b9\u7a0b\u4e0d\u80fd\u6709\u9879\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce7d7fd003c1b94cfc8c5c46f148f714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u5fc5\u987b\u4e3a\u6b63\uff1a<\/span> <\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffc789338787de266be2abc66e24a455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{A}{2}\\right)^2+\\left(\\frac{B}{2}\\right)^2-C>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"otros-tipos-de-ecuaciones-de-la-circunferencia\"><\/span>\u5176\u4ed6\u7c7b\u578b\u7684\u5706\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u89c1\u8fc7\u7684\u4e24\u4e2a\u5706\u65b9\u7a0b\uff0c\u5373\u666e\u901a\u65b9\u7a0b\u548c\u4e00\u822c\u65b9\u7a0b\uff0c\u6700\u5e38\u7528\u4e8e\u5728\u6570\u5b66\u4e0a\u8868\u8fbe\u5e73\u9762\u4e0a\u7684\u5706\uff08\u5728 R2 \u4e2d\uff09\u3002\u7136\u800c\uff0c\u6709\u51e0\u79cd\u7c7b\u578b\u7684\u65b9\u7a0b\u6765\u63cf\u8ff0\u8fd9\u4e2a\u51e0\u4f55\u5bf9\u8c61\uff0c\u4e0b\u9762\u662f\u6bcf\u79cd\u65b9\u7a0b\u7684\u89e3\u91ca\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-de-la-circunferencia\"><\/span>\u5706\u7684\u6b63\u5219\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5706\u7684\u6b63\u5219\u65b9\u7a0b\u6216\u7b80\u5316\u65b9\u7a0b\u7528\u4e8e\u63cf\u8ff0\u5176<strong>\u4e2d\u5fc3\u4f4d\u4e8e\u5750\u6807\u539f\u70b9<\/strong>\uff08\u5373\u70b9 (0,0)\uff09\u7684\u4efb\u4f55\u5706\u3002\u6240\u8ff0\u65b9\u7a0b\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8837a5c798c950520f838adb2826aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u53e6\u5916\uff0c\u5982\u679c\u534a\u5f84\u7b49\u4e8e\u5355\u4f4d\uff081\uff09\uff0c\u5219\u5468\u957f\u65b9\u7a0b\u5c06\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6638c5ad97a435df56133e8b04c26ff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u5bf9\u5e94\u4e8e\u6d4b\u89d2\u5468\u957f\uff0c\u4e5f\u79f0\u4e3a\u5355\u4f4d\u5468\u957f\u6216\u5355\u4f4d\u5706\u3002\u5b83\u662f\u4ee5\u5750\u6807\u539f\u70b9\u4e3a\u5706\u5fc3\u3001\u534a\u5f84\u4e3a 1 \u7684\u5706\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuaciones-de-dos-circunferencias-concentricas\"><\/span>\u4e24\u4e2a\u540c\u5fc3\u5706\u7684\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e24\u4e2a\u540c\u5fc3\u65b9\u7a0b\u662f\u4e2d\u5fc3\u5728\u540c\u4e00\u70b9\u7684\u65b9\u7a0b\u3002\u4e24\u4e2a\u540c\u5fc3\u5706\u552f\u4e00\u4e0d\u540c\u7684\u662f\u534a\u5f84\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\uff0c<strong>\u4e24\u4e2a\u540c\u5fc3\u5706\u7684\u65b9\u7a0b\u9664\u4e86\u72ec\u7acb\u9879\u5fc5\u987b\u4e0d\u540c\u4e4b\u5916\uff0c\u5b8c\u5168\u76f8\u540c\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8890b7cc400fafc2f805ca67e08881ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0ebfea4141df270980aa34c849d6cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4e24\u4e2a\u5706\u662f\u540c\u5fc3\u7684\uff0c\u56e0\u4e3a\u9664\u4e86\u72ec\u7acb\u9879\u4e4b\u5916\uff0c\u5b83\u4eec\u7684\u6240\u6709\u7cfb\u6570\u90fd\u76f8\u540c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7da3e573efeee0a54f17639bb938d787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+3x-4y+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e569a0908d1a2537bf5dd0d5fcaa76bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+3x-4y+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-parametrica-de-la-circunferencia\"><\/span>\u5706\u7684\u53c2\u6570\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e0e\u76f4\u7ebf\u4e00\u6837\uff0c\u5706\u7684\u65b9\u7a0b\u4e5f\u53ef\u4ee5\u7528\u6b63\u5f26\u548c\u4f59\u5f26\u7684\u4e09\u89d2\u51fd\u6570\u6765\u53c2\u6570\u5316\u3002\u56e0\u6b64\uff0c\u5706\u7684\u53c2\u6570\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-72dae5b3c5f775661ecb102945bb3fbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\diplaystyle \\begin{cases}x= a + r \\cdot \\text{cos}(t) \\\\[2ex] y= b + r\\cdot \\text{sen}(t)\\end{cases} \\qquad t\\in[0,2\\pi)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"275\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u70b9\u5728\u54ea\u91cc<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe11303e9d78d9884d5ce80743b4e853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u5706\u7684\u4e2d\u5fc3\u5e76\u4e14<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd9\u662f\u4f60\u7684\u90e8\u95e8\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-de-una-circunferencia\"><\/span>\u89e3\u51b3\u4e86\u5706\u7684\u65b9\u7a0b\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u70b9\u4e3a\u5706\u5fc3\u3001\u534a\u5f84\u4e3a5\u7684\u5706\u7684\u4e00\u822c\u65b9\u7a0b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5fa41d0801e98e2a7874c963fff73d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(-1,2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u6c42\u5706\u7684\u4e00\u822c\u65b9\u7a0b\uff0c\u9996\u5148\u8981\u6c42\u5b83\u7684\u5e38\u65b9\u7a0b\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u5706\u7684\u666e\u901a\u65b9\u7a0b\u7684\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6aaa336cc3cb4df0e6bfe594bb6e7d22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-(-1))^2+(y-2)^2=5^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"211\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2647ce60ac9f3b4bddf17ded227da332_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+1)^2+(y-2)^2=25\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u666e\u901a\u65b9\u7a0b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u627e\u5230\u5706\u7684\u4e00\u822c\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dacb70230bf38f0719ef399c3bf97727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+1^2+2\\cdot x \\cdot 1+y^2+2^2-2\\cdot y \\cdot 2=25\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"323\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c540e082018d26478d17e7cd1991280e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+1+2x+y^2+4-4y=25\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a84db66d6be46dcd6577bc788051cc6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x+y^2-4y+1+4-25=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"270\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61dbc21597fd549b0826f81395467ae8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x+y^2-4y-20=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0aad138d023e75ed59b3fa7b89247ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^2+y^2+2x-4y-20=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u5bf9\u4e8e\u4ee5\u4e0b\u6bcf\u4e2a\u5706\uff0c\u627e\u5230\u5176\u5706\u5fc3\u7684\u5750\u6807\u548c\u534a\u5f84\u7684\u957f\u5ea6\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-93caa68e4fb4ec47816d1d8e6bf3a406_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ (x-2)^2+(y+5)^2=36\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb7951cbb0d649bd68e0a7be0d66281c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\  x^2+y^2+8x-10y+1 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"234\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b63bd92988f9ebb0e256e7b6f72120e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ x^2+y^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u5468\u957fA)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8c045e659d071fcc7f64053f6be107f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-2)^2+(y+5)^2=36\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"186\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5468\u957f\u4ee5\u5e38\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5706\u5fc3\u5750\u6807\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f5efef3ea46a765419553313f5ca6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aeae2f2253b0e865affe7eb4e4045c5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{C(2,-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u534a\u5f84\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-600a7310c5834d8d3fad25e89deba0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=36\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9233e539f37236d7548131ed75ad1e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{r=6}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<hr class=\"wp-block-separator has-text-color has-pale-cyan-blue-color has-css-opacity has-pale-cyan-blue-background-color has-background\">\n<p class=\"has-text-align-left\"><strong>\u5468\u957f B)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-253fa91392e1e066a52be943874175cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+8x-10y+1 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u5468\u957f\u4ee5\u4e00\u822c\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u56e0\u6b64\u8981\u8ba1\u7b97\u5176\u4e2d\u5fc3\u7684\u5750\u6807\uff0c\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e64305413efd35fdc4d0650acf78623d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(-\\frac{A}{2}, -\\frac{B}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"111\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-554c02287c317db9bfad3ee656ffc4d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(-\\frac{8}{2}, -\\frac{-10}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"124\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e07d270b9ef4a798ab46911132c60bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\bigl(-4, -(-5)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"110\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eb4c6f0c580fa8cd0304d95339f1e49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{C(-4, 5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u6c42\u5706\u534a\u5f84\u7684\u516c\u5f0f\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0cdc38937e6c36bb9e6d2ca0814a650_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} r &amp; = \\sqrt{\\left(\\frac{A}{2}\\right)^2 +\\left(\\frac{B}{2}\\right)^2-C} \\\\[2ex] &amp; =\\sqrt{\\left(\\frac{8}{2}\\right)^2 +\\left(\\frac{-10}{2}\\right)^2-1} \\\\[2ex] &amp; =\\sqrt{\\left(4\\right)^2 +\\left(-5\\right)^2-1} \\\\[2ex] &amp;= \\sqrt{16+25-1} \\\\[2ex] &amp;= \\bm{\\sqrt{40}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"269\" width=\"218\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u5468\u957fC)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91652bf524a31b3abfbacf829d5c3024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5468\u957f\u4ee5\u5e38\u65b9\u7a0b\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5706\u5fc3\u5750\u6807\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f5efef3ea46a765419553313f5ca6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u65b9\u7a0b\u6ca1\u6709\u9879\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e24\u8005\u90fd\u4e0d<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a521efcd0a946cd643aebe98b5b41a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u56e0\u6b64\u5b83\u4ee5\u5750\u6807\u539f\u70b9\u4e3a\u4e2d\u5fc3\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-af6eeb157115e2a18cfa38f09fc11d85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{C(0,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u534a\u5f84\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f15f619bc019d0f668cff042ed62ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4964d8cfd7ef22134e4d600697e4841d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{r=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4e0b\u5217\u54ea\u4e2a\u65b9\u7a0b\u662f\u5706\u7684\u65b9\u7a0b\uff1f <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-669f1a6230f3055c7cb7a40db679ef48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ x^2+y^2+4x-6y-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"226\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef04a07d4a0089b39ecbc9de3047c185_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\  x^2+y^2+5x+5y+2xy-4 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"276\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdd38651c9b1ac5cbfc2315da374ead6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ 2x^2+2y^2-8x+4y+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f222b1efd24b2c061b293b5d0d12a374_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ x^2+y^2+x+2y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"218\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5bf9\u4e8e\u5706\u65b9\u7a0b\u7684\u8868\u8fbe\u5f0f\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n<p class=\"has-text-align-left\"> <strong>1.<\/strong>\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u7684<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5b83\u4eec\u5fc5\u987b\u7b49\u4e8e 1\u3002<br \/> <strong>2.<\/strong>\u65b9\u7a0b\u4e0d\u80fd\u6709\u9879<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce7d7fd003c1b94cfc8c5c46f148f714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p><strong>3.<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffc789338787de266be2abc66e24a455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{A}{2}\\right)^2+\\left(\\frac{B}{2}\\right)^2-C>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u9a8c\u8bc1\u6bcf\u4e2a\u65b9\u7a0b\u662f\u5426\u6ee1\u8db3\u8fd9\u4e09\u4e2a\u6761\u4ef6\u3002 <\/p>\n<hr class=\"wp-block-separator has-text-color has-pale-cyan-blue-color has-css-opacity has-pale-cyan-blue-background-color has-background\">\n<p class=\"has-text-align-left\"><strong>\u65b9\u7a0bA\uff09<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a6a81516c0f8432b89f8bc6f90ac9812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+4x-6y-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7684\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4e3a 1 \u5e76\u4e14\u65b9\u7a0b\u6ca1\u6709\u9879<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce7d7fd003c1b94cfc8c5c46f148f714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u68c0\u67e5\u7b2c\u4e09\u4e2a\u6761\u4ef6\u5c31\u8db3\u591f\u4e86\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffc789338787de266be2abc66e24a455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{A}{2}\\right)^2+\\left(\\frac{B}{2}\\right)^2-C>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48023f09730538bbe1c444ce95734453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{4}{2}\\right)^2+\\left(\\frac{-6}{2}\\right)^2-(-1)>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;216&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ef2259d5b4e8e18842abbb767a7b293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2^2+\\left(-3\\right)^2+1>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;22&#8243; width=&#8221;146&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59ef896ffd96e877fbf3198732f2d3af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 4+9+1>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;103&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91029a12fff0b2f34276f8692b5173a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 14>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;49&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u65b9\u7a0b\u6ee1\u8db33\u4e2a\u6761\u4ef6\uff0c<strong>\u6545\u4e3a\u5706\u65b9\u7a0b\u3002<\/strong> <\/p>\n<hr class=\"wp-block-separator has-text-color has-pale-cyan-blue-color has-css-opacity has-pale-cyan-blue-background-color has-background\">\n<p class=\"has-text-align-left\"><strong>\u65b9\u7a0b B)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-326811b6b97f9ba0bc878dfcf8904b21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+5x+5y+2xy-4 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"250\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u65b9\u7a0b\u6709\u4e00\u4e2a\u9879<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0b5b65b4fa8aef2ecb83e4724b75cc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5176\u4e2d\u65b9\u7a0b<strong>\u4e0d\u5bf9\u5e94\u4e8e\u5706\u3002<\/strong> <\/p>\n<hr class=\"wp-block-separator has-text-color has-pale-cyan-blue-color has-css-opacity has-pale-cyan-blue-background-color has-background\">\n<p class=\"has-text-align-left\"><strong>\u65b9\u7a0bC)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7997d025687293da234c60efbb4390ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^2+2y^2-8x+4y+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"218\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7684\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4e0d\u662f 1\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9664\u4ee5\u6240\u6709\u9879\u6765\u53d8\u6362\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-324f0e4c339c56376f79a6f8420fcb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2-4x+2y+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u6837\u73b0\u5728\u7684\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u7684\uff0c\u5b83\u4eec\u662f 1\uff0c\u800c\u4e14\uff0c\u65b9\u7a0b\u6ca1\u6709\u9879<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce7d7fd003c1b94cfc8c5c46f148f714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u9a8c\u8bc1\u7b2c\u4e09\u4e2a\u6761\u4ef6\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffc789338787de266be2abc66e24a455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{A}{2}\\right)^2+\\left(\\frac{B}{2}\\right)^2-C>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-283fb580944e951ece8b8e24e84eb524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{-4}{2}\\right)^2+\\left(\\frac{2}{2}\\right)^2+1>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;189&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91f0622656a691a59a0e9052709d21de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (-2)^2+\\left(1\\right)^2+1>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;22&#8243; width=&#8221;158&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5eadfd980efe34932b4329383d30563a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 4+1+1>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;103&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8c570dbdfdce26cd5e1e13bd563e2ccd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 6>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;42&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u65b9\u7a0b\u6ee1\u8db33\u4e2a\u6761\u4ef6\uff0c<strong>\u6545\u4e3a\u5706\u65b9\u7a0b\u3002<\/strong> <\/p>\n<hr class=\"wp-block-separator has-text-color has-pale-cyan-blue-color has-css-opacity has-pale-cyan-blue-background-color has-background\">\n<p class=\"has-text-align-left\"><strong>\u65b9\u7a0b D)<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b896c6512c871afb6136853a0a2cf72b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+x+2y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"191\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7684\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76e092d71026e8d64e9e3fc6857554cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c73c29a3e05add4949b9207310200e96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4e3a 1 \u5e76\u4e14\u65b9\u7a0b\u6ca1\u6709\u9879<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce7d7fd003c1b94cfc8c5c46f148f714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"xy.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u68c0\u67e5\u7b2c\u4e09\u4e2a\u6761\u4ef6\u5c31\u8db3\u591f\u4e86\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffc789338787de266be2abc66e24a455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{A}{2}\\right)^2+\\left(\\frac{B}{2}\\right)^2-C>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df508b8ad2882f89d197f3845bcc13ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{1}{2}\\right)^2+\\left(\\frac{2}{2}\\right)^2-6>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;47&#8243; width=&#8221;175&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06600177f85089d43db1d30e47297e6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0,25+1-6>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;128&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74d079e75c8619832a03cd179a3383ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -4,75 \\ \\cancel{>} \\ 0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;82&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u65b9\u7a0b\u4e0d\u6ee1\u8db3\u6700\u540e\u4e00\u4e2a\u6761\u4ef6\uff0c\u56e0\u6b64<strong>\u5b83\u4e0d\u662f\u5706\u7684\u65b9\u7a0b<\/strong>\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u786e\u5b9a\u7ecf\u8fc7\u4e0b\u5217\u4e09\u70b9\u7684\u5706\u7684\u65b9\u7a0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4502f53d3453a32786375e0583cb2785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(0,0) \\quad B(3,0) \\quad C(2,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4efb\u610f\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8890b7cc400fafc2f805ca67e08881ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+y^2+Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5c06\u70b9\u7684\u5750\u6807\u4ee3\u5165\u5706\u65b9\u7a0b\u6765\u6c42\u53c2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94b9e9013dcf92b4ae2a6fbb804365a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A,\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e33ac8af21963090f8229a332d211273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u901a\u8fc7\u7b2c\u4e00\u70b9\u6211\u4eec\u627e\u5230\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab5bb26176c859b9b09d69eb399bea9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c994d016e5b89d5820060efa138860cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(0,0) \\ \\longrightarrow \\ 0^2+0^2+A\\cdot 0 +B\\cdot 0+C=0 \\ \\longrightarrow \\ \\bm{C = 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"437\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6839\u636e\u7b2c\u4e8c\u70b9\u6211\u4eec\u6c42\u51fa\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944477c7f7578892a57aa3b7c7dd8268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A:\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12719654d98ba81f0a7d45e587478e6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}A(3,0) \\ \\longrightarrow  \\ &amp; 3^2+0^2+A\\cdot 3 +B\\cdot 0+C=0  \\\\[2ex] &amp; 9+A\\cdot 3  =0\\\\[2ex]&amp;  \\bm{A=-3} &amp; \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"335\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4ece\u7b2c\u4e09\u70b9\u6211\u4eec\u6c42\u51fa\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2976704f0327609d6a0deba6d1139c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1e69c28996a8fbfa14189c48a295095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} A(2,-2) \\ \\longrightarrow  \\ &amp; 2^2+(-2)^2+A\\cdot 2 +B\\cdot (-2)+C=0 \\\\[2ex] &amp; 4+4+(-3)\\cdot 2+ B\\cdot (-2)+0=0 \\\\[2ex] &amp; 8-6-2B=0 \\\\[2ex] &amp; \\bm{B=1} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u603b\u4e4b\uff0c\u5468\u957f\u7684\u4e00\u822c\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9f54f4187497c1fa02459870f4738c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^2+y^2-3x+y=0}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u5982\u679c\u5706\u7684\u4e24\u7aef\u662f\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dad063e5dabd63e9833d42ad087a2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,3) \\qquad B(6,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5706\u7684\u666e\u901a\u65b9\u7a0b\u662f\u4ec0\u4e48\uff1f <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5982\u679c\u8fd9\u4e24\u70b9\u662f\u5706\u7684\u7aef\u70b9\uff0c\u5219\u5706\u5fc3\u5c06\u662f\u8fd9\u4e24\u70b9\u4e4b\u95f4\u7684\u4e2d\u70b9\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8301618bb0d7b4ded6acd02f1087b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(\\frac{2+6}{2} , \\frac{3+(-1)}{2} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"162\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe41a577fe933b35601afe7f6239e03d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(\\frac{8}{2} , \\frac{2}{2} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"73\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06be238c032f258db6686b8e2c164605_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C\\left(4,1 \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5706\u7684\u76f4\u5f84\u5c06\u662f\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e24\u70b9\u5f62\u6210\u7684\u77e2\u91cf\u7684\u5927\u5c0f\u6765\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3dd2c628d11818ba0cab76f4614ed91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B-A=(6,-1) - (2,3) = (4,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d0fb498083e41cf9f0f8b7a150f42fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d = \\lvert \\vv{AB} \\rvert =\\sqrt{4^2+(-4)^2} = \\sqrt{16+16} = \\sqrt{32}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"346\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5706\u7684\u534a\u5f84\u662f\u76f4\u5f84\u7684\u4e00\u534a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d5a6269d58490fc6848303c3654a1c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r = \\cfrac{\\sqrt{32}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5706\u7684\u666e\u901a\u65b9\u7a0b\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb8ffc83b27f7ed251e2233abbce5046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-a)^2+(y-b)^2=r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a958c8b86fa29064dff3aa581e722473_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (x-4)^2+(y-1)^2=\\left(\\frac{\\sqrt{32}}{2}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"239\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34bc4dc9c86ca1b78edaa23113e51a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{(x-4)^2+(y-1)^2=}\\frac{\\bm{32}}{\\bm{4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"183\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u6700\u540e\uff0c\u5982\u679c\u672c\u6587\u5bf9\u60a8\u6709\u7528\uff0c\u60a8\u80af\u5b9a\u4e5f\u4f1a\u5bf9\u6211\u4eec\u7684<a href=\"https:\/\/mathority.org\/cn\/\u53cc\u66f2\u7ebf\u5b9a\u4e49\u516c\u5f0f\u5143\u7d20\u65b9\u7a0b\u793a\u4f8b\u7ec3\u4e60\u5df2\u89e3\u51b3\/\">\u53cc\u66f2\u7ebf\uff08\u6570\u5b66\uff09<\/a>\u548c<a href=\"https:\/\/mathority.org\/cn\/\u629b\u7269\u7ebf\u6570\u5b66\u5b9a\u4e49\u65b9\u7a0b\u793a\u4f8b\u7ec3\u4e60\u5143\u7d20\u5df2\u89e3\u51b3\/\">\u629b\u7269\u7ebf\uff08\u6570\u5b66\uff09<\/a>\u9875\u9762\u611f\u5174\u8da3\u3002\u60a8\u5c06\u627e\u5230\u5173\u4e8e\u53cc\u66f2\u7ebf\u548c\u629b\u7269\u7ebf\u662f\u4ec0\u4e48\u3001\u5b83\u4eec\u7684\u65b9\u7a0b\u3001\u5b83\u4eec\u7684\u7279\u5f81\u3001\u793a\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u7684\u8be6\u7ec6\u89e3\u91ca&#8230;&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u5706\u5468\u65b9\u7a0b\u7684\u6240\u6709\u5185\u5bb9\uff1a\u666e\u901a\u65b9\u7a0b\u3001\u4e00\u822c\u65b9\u7a0b\u3001\u5176\u4ed6\u7c7b\u578b\u7684\u5706\u5468\u65b9\u7a0b\u3001\u4f55\u65f6\u5706\u5468\u65b9\u7a0b\u6b63\u786e\u2026\u2026\u6b64\u5916\uff0c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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