{"id":238,"date":"2023-07-10T17:01:09","date_gmt":"2023-07-10T17:01:09","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%85%ac%e5%bc%8f%e5%85%83%e7%b4%a0%e6%96%b9%e7%a8%8b%e7%a4%ba%e4%be%8b%e7%bb%83%e4%b9%a0%e5%b7%b2%e8%a7%a3%e5%86%b3\/"},"modified":"2023-07-10T17:01:09","modified_gmt":"2023-07-10T17:01:09","slug":"%e5%8f%8c%e6%9b%b2%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%85%ac%e5%bc%8f%e5%85%83%e7%b4%a0%e6%96%b9%e7%a8%8b%e7%a4%ba%e4%be%8b%e7%bb%83%e4%b9%a0%e5%b7%b2%e8%a7%a3%e5%86%b3","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%85%ac%e5%bc%8f%e5%85%83%e7%b4%a0%e6%96%b9%e7%a8%8b%e7%a4%ba%e4%be%8b%e7%bb%83%e4%b9%a0%e5%b7%b2%e8%a7%a3%e5%86%b3\/","title":{"rendered":"\u5938\u5f20\uff1a\u5b9a\u4e49\u3001\u516c\u5f0f\u3001\u5143\u7d20\u3001\u65b9\u7a0b\u5f0f\u3001\u793a\u4f8b\u2026\u2026"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u53cc\u66f2\u7ebf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u662f\u4ec0\u4e48\u3001\u5b83\u7684\u7279\u5f81\u5143\u7d20\u662f\u4ec0\u4e48\u3001\u5982\u4f55\u627e\u5230\u5b83\u7684\u65b9\u7a0b\u3001\u793a\u4f8b\u3001\u5df2\u89e3\u7b54\u7684\u7ec3\u4e60\u7b49\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-hiperbola\"><\/span>\u4ec0\u4e48\u662f\u5938\u5f20\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-93\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p>\u53cc\u66f2\u7ebf\u662f\u4e00\u6761\u6709\u4e24\u4e2a\u5206\u652f\u7684\u5f00\u66f2\u7ebf\uff0c\u5176\u6570\u5b66\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p><strong>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u53cc\u66f2\u7ebf\u662f\u5e73\u9762\u4e0a\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u70b9\u7684\u8f68\u8ff9\uff1a\u53cc\u66f2\u7ebf\u4e0a\u7684\u4efb\u610f\u70b9\u4e0e\u4e24\u4e2a\u56fa\u5b9a\u70b9\uff08\u79f0\u4e3a\u7126\u70b9\uff09\u4e4b\u95f4\u7684\u8ddd\u79bb\u5dee\u7684\u7edd\u5bf9\u503c\u5fc5\u987b\u6052\u5b9a\u3002<\/strong><\/p>\n<p>\u6b64\u5916\uff0c\u8fd9\u4e24\u4e2a\u8ddd\u79bb\u76f8\u51cf\u7684\u503c\u59cb\u7ec8\u7b49\u4e8e\u53cc\u66f2\u7ebf\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\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-08f25424560ca1e7449189d00268f0b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert d_1 - d_2 \\rvert = 2a\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/definition-dhyperbole.webp\" alt=\"\u5938\u5f20\u7684\u5b9a\u4e49\" class=\"wp-image-2260\" width=\"411\" height=\"377\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<p>\u4e0b\u9762\u6211\u4eec\u6765\u770b\u770b\u7cfb\u6570\u7684\u542b\u4e49<\/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>\u4e00\u4e2a\u5938\u5f20\u7684\u8bf4\u6cd5\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-96\">\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:33.33%\">\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\/hyperbole-conique.webp\" alt=\"\u5706\u9525\u53cc\u66f2\u7ebf\u6216\u5706\u9525\u66f2\u7ebf\" class=\"wp-image-2272\" width=\"307\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\"flex-basis:66.66%\">\n<p>\u6b64\u5916\uff0c\u53cc\u66f2\u7ebf\u4e0e\u5706\u5468\u3001\u692d\u5706\u548c\u629b\u7269\u7ebf\u4e00\u8d77\u5c5e\u4e8e\u79f0\u4e3a\u4e8c\u6b21\u66f2\u7ebf\u7684\u51e0\u4f55\u7fa4\u7684\u4e00\u90e8\u5206\u3002\u56e0\u6b64\uff0c\u53cc\u66f2\u7ebf\u662f\u5706\u9525\u66f2\u7ebf\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u53ef\u4ee5\u7531\u5706\u9525\u5f97\u5230\u3002<\/p>\n<p>\u7279\u522b\u5730\uff0c\u53cc\u66f2\u7ebf\u662f\u5706\u9525\u4f53\u88ab\u5e73\u9762\u622a\u65ad\u7684\u7ed3\u679c\uff0c\u8be5\u5e73\u9762\u7684\u89d2\u5ea6\u5c0f\u4e8e\u5706\u9525\u4f53\u7684\u6bcd\u7ebf\u76f8\u5bf9\u4e8e\u5176\u65cb\u8f6c\u8f74\u5f62\u6210\u7684\u89d2\u5ea6\u3002 <\/p>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"elementos-de-una-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u7684\u8981\u7d20<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53cc\u66f2\u7ebf\u7684\u7279\u5f81\u53d6\u51b3\u4e8e\u4ee5\u4e0b\u56e0\u7d20\uff1a<\/p>\n<ul>\n<li><strong>\u7126\u70b9<\/strong>\uff1a\u8fd9\u662f\u6bcf\u4e2a\u53cc\u66f2\u7ebf\u7684\u4e24\u4e2a\u56fa\u5b9a\u70b9\u7279\u5f81\uff08\u4e0b\u56fe\u4e2d\u7684\u70b9 F \u548c F&#8217;\uff09\u3002\u53cc\u66f2\u7ebf\u4efb\u610f\u70b9\u5230\u6bcf\u4e2a\u7126\u70b9\u7684\u8ddd\u79bb\u5dee\u7684\u7edd\u5bf9\u503c\u6052\u5b9a\u4e14\u7b49\u4e8e\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54b4363957caf696f4e42af854400e03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li><strong>\u7126\u70b9\u6216\u4e3b\u8f74<\/strong>\uff1a\u7a7f\u8fc7\u53cc\u66f2\u7ebf\u4e24\u4e2a\u7126\u70b9\u7684\u7ebf\u3002\u5b83\u5bf9\u5e94\u4e8e\u6240\u8ff0\u51e0\u4f55\u56fe\u5f62\u7684\u5bf9\u79f0\u8f74\u3002\u4e5f\u79f0\u4e3a\u6a2a\u8f74\u6216\u6a2a\u8f74\u3002<\/li>\n<li><strong>\u6b21\u8f74<\/strong>\uff1a\u5b83\u662f\u7ebf\u6bb5 FF&#8217; \u7684\u5e73\u5206\u7ebf\uff08\u901a\u8fc7\u70b9 B \u548c B&#8217; \u7684\u7ebf\uff09\u3002\u53e6\u5916\uff0c\u5b83\u662f\u4e00\u6761\u5782\u76f4\u4e8e\u7126\u8f74\u7684\u7ebf\uff0c\u5b83\u662f\u53cc\u66f2\u7ebf\u7684\u53e6\u4e00\u4e2a\u5bf9\u79f0\u8f74<\/li>\n<li><strong>\u4e2d\u5fc3\uff08O\uff09<\/strong> \uff1a\u662f\u4e24\u4e2a\u8f74\u7684\u4ea4\u70b9\u4ee5\u53ca\u4e24\u4e2a\u9876\u70b9\u548c\u4e24\u4e2a\u7126\u70b9\u7684\u4e2d\u70b9\u3002\u7531\u4e8e\u53cc\u66f2\u7ebf\u6709\u4e24\u4e2a\u5bf9\u79f0\u8f74\uff0c\u56e0\u6b64\u5b83\u4e5f\u662f\u5bf9\u79f0\u4e2d\u5fc3\u3002<\/li>\n<li><strong>\u9876\u70b9\uff08A\u548cA&#8217;\uff09<\/strong> \uff1a\u662f\u53cc\u66f2\u7ebf\u7684\u5206\u652f\u4e0e\u7126\u8f74\u7684\u4ea4\u70b9\u3002<\/li>\n<li><strong>\u77e2\u91cf\u5c04\u7ebf (R)<\/strong> \uff1a\u8fd9\u4e9b\u662f\u4ece\u53cc\u66f2\u7ebf\u4e0a\u7684\u4efb\u610f\u70b9\u5230\u6bcf\u4e2a\u7126\u70b9\u7684\u7ebf\u6bb5\u3002<\/li>\n<li><strong>\u7126\u8ddd<\/strong>\uff1a\u8fd9\u662f\u4e24\u4e2a\u7126\u70b9\u4e4b\u95f4\u7684\u590d\u5408\u6bb5\u7684\u957f\u5ea6\u3002<\/li>\n<li><strong>\u957f\u8f74\u6216\u5b9e\u8f74\uff1a<\/strong>\u4eceA\u70b9\u5230A&#8217;\u70b9\u7684\u7ebf\u6bb5\uff0c\u5176\u957f\u5ea6\u7b49\u4e8e\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54b4363957caf696f4e42af854400e03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li><strong>\u5c0f\u8f74\u6216\u865a\u8f74\uff1a<\/strong>\u4eceB\u70b9\u5230B&#8217;\u70b9\u7684\u7ebf\u6bb5\uff0c\u5176\u957f\u5ea6\u7b49\u4e8e\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d8ead68299e64ffadc626710518ae55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2b.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li><strong>\u6e10\u8fd1\u7ebf<\/strong>\uff1a\u662f\u56fe\u8868\u4e0a\u663e\u793a\u7684\u865a\u7ebf\u3002\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u770b\u5230\u5b83\u4eec\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002 <\/li>\n<\/ul>\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\/elements-de-l-hyperbole.webp\" alt=\"\u53cc\u66f2\u7ebf\u7684\u5143\u7d20\" class=\"wp-image-2276\" width=\"433\" height=\"396\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relacion-entre-los-elementos-de-una-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u5404\u5143\u7d20\u4e4b\u95f4\u7684\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u9996\u5148\u6211\u4eec\u8bf4\u7684\u534a\u8f74\u662f\u6307\u534a\u4e2a\u8f74\u3002\u4f8b\u5982\uff0c\u771f\u534a\u8f74\u662f\u4eceA\u70b9\u5230\u53cc\u66f2\u7ebf\u4e2d\u5fc3\u7684\u7ebf\u6bb5\uff0c\u5176\u957f\u5ea6\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-2ebc59bdf10d3d739bfa532b65c85287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5b9e\u534a\u8f74\u3001\u865a\u534a\u8f74\u548c\u534a\u7126\u8ddd\u4e4b\u95f4\u5b58\u5728\u7740\u975e\u5e38\u91cd\u8981\u7684\u5173\u7cfb\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u8981\u63a8\u5bfc\u7684\u516c\u5f0f\u88ab\u5927\u91cf\u7528\u4e8e\u89e3\u51b3\u53cc\u66f2\u7ebf\u7ec3\u4e60\u548c\u95ee\u9898\u3002<\/p>\n<p>\u8981\u77e5\u9053\uff0c\u53cc\u66f2\u7ebf\u7684 B \u70b9\u548c B&#8217; \u70b9\u5bf9\u5e94\u4e8e\u4e3b\u8f74\u4e0e\u5047\u60f3\u534a\u5f84\u5706\u7684\u4ea4\u70b9<\/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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4ece\u4e2d\u5fc3\u5230 A \u70b9\uff08\u534a\u7126\u8ddd\uff09\u3002\u56e0\u6b64\uff0c\u6b63\u5982\u60a8\u5728\u4e0b\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\u770b\u5230\u7684\uff0c\u8fde\u63a5 A \u70b9\u548c B \u70b9\u7684\u7ebf\u6bb5\u4e0e\u6240\u8ff0\u5706\u7684\u534a\u5f84\u91cd\u5408\uff08<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \uff09\uff1a <\/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\/elements-de-relation-dune-hyperbole.webp\" alt=\"\u53cc\u66f2\u7ebf\u5404\u5143\u7d20\u4e4b\u95f4\u7684\u5173\u7cfb\" class=\"wp-image-2282\" width=\"433\" height=\"398\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\u7531\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\u53ef\u4ee5\u8bc1\u660e\u53c2\u6570\u4e4b\u95f4\u7684\u5173\u7cfb<\/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-0357ced152d91599aefcf60b48861b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a, b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\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-6d7a13f23d60337d2591c3d955d44faf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c^2 = a^2+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-la-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53cc\u66f2\u7ebf\u65b9\u7a0b\u6709\u591a\u79cd\u7c7b\u578b\uff0c\u56e0\u4e3a\u6839\u636e\u5176\u6027\u8d28\uff0c\u53ef\u4ee5\u4f7f\u7528\u5176\u4e2d\u4e00\u79cd\u6216\u53e6\u4e00\u79cd\u6765\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u5b83\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u9010\u4e00\u8be6\u7ec6\u5206\u6790\u3002<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u6709\u53cc\u66f2\u7ebf\u7684<strong>\u666e\u901a\u65b9\u7a0b<\/strong>\u3002\u5176\u6b21\uff0c\u6211\u4eec\u5c06\u770b\u5230\u666e\u901a\u65b9\u7a0b\u7684\u4e00\u4e2a\u53d8\u4f53\uff0c\u8fd9\u662f\u53cc\u66f2\u7ebf\u7684<strong>\u7b80\u5316\u65b9\u7a0b\u6216\u6b63\u5219\u65b9\u7a0b<\/strong>\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u53cc\u66f2\u7ebf\u7684<strong>\u4e00\u822c\u65b9\u7a0b<\/strong>\u662f\u5982\u4f55\u7684\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5206\u6790\u53cc\u66f2\u7ebf\u7684\u4e24\u79cd\u7279\u6b8a\u60c5\u51b5\u7684\u65b9\u7a0b\uff1a<strong>\u7b49\u8fb9\u53cc\u66f2\u7ebf<\/strong>\u548c<strong>\u5171\u8f6d\u53cc\u66f2\u7ebf<\/strong>\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-ordinaria-de-la-hiperbola\"><\/span>\u666e\u901a\u53cc\u66f2\u7ebf\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5f53\u6211\u4eec\u60f3\u8981\u901a\u8fc7\u65b9\u7a0b\u5b9a\u4e49\u4e00\u6761\u5916\u5fc3\u4f4d\u4e8e\u5750\u6807\u539f\u70b9\uff08\u70b9\uff080,0\uff09\uff09\u7684\u53cc\u66f2\u7ebf\u65f6\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\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\">\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e2d<strong>\u53cc\u66f2\u7ebf\u7684\u5e38<\/strong>\u65b9\u7a0b\u7684\u516c\u5f0f\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-2b3ab0b73fd88032017edcdc4c41fbdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x-x_0)^2}{a^2}-\\cfrac{(y-y_0)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"195\" style=\"vertical-align: -12px;\"><\/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-87f2a80bc63f8d7bc3df68c45a787402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/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-d37dc47669aa63f72480eae663d99287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u53cc\u66f2\u7ebf\u4e2d\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-47ff14e7a2fa6ff014a1fcb82ec4fd58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"O(x_0,y_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<\/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>\u662f\u53cc\u66f2\u7ebf\u7684\u534a\u957f\u8f74\u7684\u957f\u5ea6\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-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\u53cc\u66f2\u7ebf\u7684\u77ed\u534a\u8f74\u7684\u957f\u5ea6\u3002<\/li>\n<\/ul>\n<\/div>\n<p>\u901a\u8fc7\u8fd9\u4e2a\u65b9\u7a0b\uff0c\u60a8\u53ef\u4ee5\u63cf\u8ff0\u7126\u8f74\u4e3a\u6c34\u5e73\u7684\u53cc\u66f2\u7ebf\uff08\u5411\u5de6\u548c\u5411\u53f3\u6253\u5f00\u7684\u5206\u652f\uff09\uff0c\u8fd9\u5c31\u662f\u901a\u5e38\u7684\u53cc\u66f2\u7ebf\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528\u5782\u76f4\u7126\u8f74\uff08\u4ece\u4e0a\u5230\u4e0b\u6253\u5f00\u7684\u5206\u652f\uff09\uff0c\u5219\u8d1f\u53f7\u4ece\u53d8\u91cf y \u4f20\u9012<em>\u5230<\/em>\u53d8\u91cf<em>x<\/em> \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-f6f7bf1fb4ba24a25f4d33754bb31477_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(y-y_0)^2}{a^2}-\\cfrac{(x-x_0)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"195\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-87f2a80bc63f8d7bc3df68c45a787402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/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-d37dc47669aa63f72480eae663d99287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u548c\u4ee5\u524d\u4e00\u6837\uff0c\u662f\u53cc\u66f2\u7ebf\u4e2d\u5fc3\u7684\u5750\u6807\u548c\u9879<\/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>\u5b83\u4eec\u4ecd\u7136\u662f\u53cc\u66f2\u7ebf\u7684\u534a\u957f\u8f74\u548c\u534a\u77ed\u8f74\uff0c\u5c3d\u7ba1\u4e0e\u4ee5\u524d\u4e0d\u540c\uff0c\u8fd9\u4e24\u4e2a\u8f74\u73b0\u5728\u5c06\u5206\u522b\u5782\u76f4\u548c\u6c34\u5e73\u5b9a\u5411\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-canonica-o-reducida-de-la-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u7684\u6b63\u5219\u65b9\u7a0b\u6216\u7b80\u5316\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8fd9\u7c7b\u53cc\u66f2\u7ebf\u65b9\u7a0b\u4e0e\u666e\u901a\u65b9\u7a0b\u975e\u5e38\u76f8\u4f3c\uff0c\u552f\u4e00\u7684\u533a\u522b\u662f\u6b63\u5219\u65b9\u7a0b\u7528\u4e8e\u89e3\u6790\u8868\u8fbe\u4ee5\u70b9(0,0)\u4e3a\u4e2d\u5fc3\u7684\u53cc\u66f2\u7ebf\u3002\u56e0\u6b64\uff0c<strong>\u5f53\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\u662f\u5750\u6807\u539f\u70b9\u65f6\uff0c\u6211\u4eec\u4f7f\u7528\u53cc\u66f2\u7ebf\u7684\u6b63\u5219\u65b9\u7a0b\u6216\u7b80\u5316\u65b9\u7a0b\u3002<\/strong><\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u6839\u636e\u53cc\u66f2\u7ebf\u7684\u5e38\u65b9\u7a0b\u63a8\u5bfc\u51fa\u53cc\u66f2\u7ebf\u7b80\u5316\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-2b3ab0b73fd88032017edcdc4c41fbdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x-x_0)^2}{a^2}-\\cfrac{(y-y_0)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"195\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\u5e94\u4e3a\u5750\u6807\u539f\u70b9\uff0c\u5373\u70b9 (0,0)\uff0c\u5219\u4ee5\u4e0b\u60c5\u51b5\u59cb\u7ec8\u4e3a\u771f\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-f9ec62f2078baa728f7ebfabffd10153_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_0 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -3px;\"><\/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-0fe89d278351632cc7ab2e5843b59d50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_0 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u53cc\u66f2\u7ebf\u7684\u89c4\u8303\u6216\u7b80\u5316\u65b9\u7a0b\u516c\u5f0f\u5c06\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-653c6439435e1d76761300f67aa939d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{\\color{black}\\qquad\\cfrac{x^2}{a^2}-\\cfrac{y^2}{b^2} = 1 \\vphantom{\\cfrac{\\vphantom{\\Bigl(}}{\\vphantom{\\Bigl(}}}\\qquad }\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"270\" style=\"vertical-align: -35px;\"><\/p>\n<\/p>\n<p>\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u5982\u679c\u7126\u8f74\u662f\u5782\u76f4\u7684\u800c\u4e0d\u662f\u6c34\u5e73\u7684\uff0c\u5219\u8d1f\u53d8\u91cf\u5c06\u4e3a<em>x<\/em> \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-1d89d30363f5d7ac5992b0d9d8e4397d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{y^2}{a^2}-\\cfrac{x^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-general-de-la-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u53cc\u66f2\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b\u7684\u516c\u5f0f\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-e8e106cce0aeffcded8cfba226c6dc22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax^2 +Bxy+Cy^2 +Dx+Ey+F =0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7136\u800c\uff0c\u4e3a\u4e86\u4f7f\u4e0a\u5f0f\u6210\u4e3a\u53cc\u66f2\u7ebf\uff0c\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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" 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-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4eec\u5fc5\u987b\u4e0d\u540c\u4e8e\u96f6\uff0c\u540c\u65f6\u5177\u6709\u76f8\u53cd\u7684\u7b26\u53f7\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-la-hiperbola-equilatera\"><\/span>\u7b49\u8fb9\u53cc\u66f2\u7ebf\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u7b49\u8fb9\u53cc\u66f2\u7ebf<\/strong>\u662f\u5b9e\u534a\u8f74\u957f\u5ea6\u7b49\u4e8e\u865a\u534a\u8f74\u957f\u5ea6\u7684\u53cc\u66f2\u7ebf\uff0c\u8fd9\u610f\u5473\u7740<\/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-76d8257c341ab795017e6ec1e1565889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=b.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u7b49\u8fb9\u53cc\u66f2\u7ebf\u7684\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-41a889e08f8508111c6947103382ea8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{a^2}-\\cfrac{y^2}{a^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6b64\u5916\uff0c\u7b49\u8fb9\u53cc\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf\u5f7c\u6b64\u5782\u76f4\u3002\u8fd9\u4e9b\u7ebf\u7684\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-0a99c26c04ea6299b78366ce136d5675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" 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-a174c09e7d620501dd0fce5f658bb9a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u8fd9\u4e24\u4e2a\u65b9\u7a0b\u5206\u522b\u662f\u7b2c\u4e00\uff08\u548c\u7b2c\u4e09\uff09\u8c61\u9650\u548c\u7b2c\u4e8c\uff08\u548c\u7b2c\u56db\uff09\u8c61\u9650\u7684\u5e73\u5206\u7ebf\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5c06\u7b49\u8fb9\u53cc\u66f2\u7ebf\u5411\u5de6\u65cb\u8f6c 45\u00b0\uff0c\u5219\u5b83\u7684\u6e10\u8fd1\u7ebf\u5360\u636e\u5750\u6807\u8f74\u7684\u4f4d\u7f6e\uff1a <\/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-hyperbole-equilaterale.webp\" alt=\"\u7b49\u8fb9\u53cc\u66f2\u7ebf\u65b9\u7a0b\" class=\"wp-image-2304\" width=\"468\" height=\"425\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u5f53\u6211\u4eec\u8fdb\u884c 45\u00b0 \u8f6c\u5f2f\u65f6\uff0c\u53cc\u66f2\u7ebf\u7684\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-7d1ceb65ffe8df5812631035e3716fef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\cdot y = \\cfrac{a^2}{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hiperbolas-conjugadas\"><\/span>\u5171\u8f6d\u53cc\u66f2\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5982\u679c\u4e00\u6761\u53cc\u66f2\u7ebf\u7684\u5b9e\u8f74\u7b49\u4e8e\u53e6\u4e00\u6761\u53cc\u66f2\u7ebf\u7684\u865a\u8f74\uff0c\u5219\u4e24\u6761\u53cc\u66f2\u7ebf\u662f\u5171\u8f6d\u7684<\/strong>\u3002\u56e0\u6b64\uff0c\u4e24\u4e2a\u5171\u8f6d\u53cc\u66f2\u7ebf\u65b9\u7a0b\u4e4b\u95f4\u7684\u552f\u4e00\u533a\u522b\u5728\u4e8e\u54ea\u4e2a\u53d8\u91cf\u88ab\u5426\u5b9a\uff0c\u56e0\u4e3a\u5206\u6bcd\u7684\u7cfb\u6570\u5fc5\u987b\u4fdd\u6301\u76f8\u540c\u3002<\/p>\n<p>\u8fd9\u662f\u4e24\u4e2a\u5f7c\u6b64\u5171\u8f6d\u7684\u53cc\u66f2\u7ebf\u65b9\u7a0b\u7684\u793a\u4f8b\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-1d53db10e1f9803780acbba6c67d420b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{a^2} - \\cfrac{y^2}{b^2}=1 \\qquad \\qquad  \\cfrac{y^2}{b^2}-\\cfrac{x^2}{a^2} =1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"254\" style=\"vertical-align: -12px;\"><\/p>\n<\/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-des-hyperboles-conjuguees.webp\" alt=\"\u5171\u8f6d\u53cc\u66f2\u7ebf\u65b9\u7a0b\" class=\"wp-image-2308\" width=\"430\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6b64\u5916\uff0c\u4ece\u7ed8\u5236\u7684\u53cc\u66f2\u7ebf\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u5171\u8f6d\u53cc\u66f2\u7ebf\u5177\u6709\u76f8\u540c\u7684\u6e10\u8fd1\u7ebf\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"asintotas-de-la-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u56fe\u8868\u4e2d\u770b\u5230\u7684\uff0c\u6bcf\u4e2a\u53cc\u66f2\u7ebf\u90fd\u6709\u4e24\u6761\u6e10\u8fd1\u7ebf\u3002\u8bf7\u8bb0\u4f4f\uff0c\u6e10\u8fd1\u7ebf\u662f\u4e00\u6761\u975e\u5e38\u63a5\u8fd1\u51fd\u6570\u4f46\u4ece\u672a\u5b8c\u5168\u76f8\u4ea4\u6216\u63a5\u89e6\u7684\u76f4\u7ebf\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5bf9\u5e94\u4e8e\u53cc\u66f2\u7ebf\u6e10\u8fd1\u7ebf\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-4d50d6c5ebf08aabc0b03be7e7bac218_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{b}{a} x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"54\" style=\"vertical-align: -12px;\"><\/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-ecebcdc0521000a1f941340fd05f84a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -\\cfrac{b}{a}x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"68\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u4efb\u4f55\u53cc\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf\u90fd\u53ef\u4ee5\u4f7f\u7528\u5b83\u4eec\u7684\u7cfb\u6570\u8f7b\u677e\u786e\u5b9a<\/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>\u548c<\/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>\u5206\u522b\u662f\u53cc\u66f2\u7ebf\u7684\u5b9e\u534a\u8f74\u548c\u865a\u534a\u8f74\u7684\u957f\u5ea6\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"excentricidad-de-la-hiperbola\"><\/span>\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387<\/strong>\u662f\u51b3\u5b9a\u5176\u5f00\u653e\u6216\u95ed\u5408\u7a0b\u5ea6\u7684\u7279\u5f81\u53c2\u6570\u3002\u5728\u6570\u503c\u4e0a\uff0c\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387\u662f\u901a\u8fc7\u5c06\u5176\u534a\u7126\u8ddd\u9664\u4ee5\u5176\u5b9e\u534a\u8f74\u6765\u8ba1\u7b97\u7684\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-7290cf41b85af2331d8634e251ca44b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=\\cfrac{c}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4efb\u4f55\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387\u603b\u662f\u5927\u4e8e 1\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-47a5ae71a1f4a771f6017b1fc5600ec4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;40&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p>\u8be5\u53c2\u6570\u7684\u503c\u975e\u5e38\u76f8\u5173\uff0c\u56e0\u4e3a\u5b83\u6307\u793a\u7ed9\u5b9a\u53cc\u66f2\u7ebf\u7684\u5f62\u72b6\u3002\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387\u8d8a\u63a5\u8fd11\uff0c\u5176\u5206\u652f\u8d8a\u95ed\u5408\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u504f\u5fc3\u7387\u7684\u503c\u8d8a\u5927\uff0c\u5176\u5206\u652f\u5c31\u8d8a\u5f20\u5f00\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\/excentricite-dune-hyperbole.webp\" alt=\"\u5938\u5f20\u7684\u504f\u5fc3\u7387\" class=\"wp-image-2314\" width=\"413\" height=\"182\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6700\u540e\uff0c\u5e94\u8be5\u6ce8\u610f\u7684\u662f\uff0c\u7b49\u8fb9\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387\u59cb\u7ec8\u7b49\u4e8e<\/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-dcc432e053b2cf0b17f199b8eb91ab1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{2}.\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"27\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-hiperbolas\"><\/span>\u53cc\u66f2\u7ebf\u95ee\u9898\u5df2\u89e3\u51b3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0b\u9762\u4f60\u53ef\u4ee5\u7ec3\u4e60\u6211\u4eec\u5728\u53cc\u66f2\u7ebf\u548c\u53cc\u66f2\u7ebf\u65b9\u7a0b\u7684\u95ee\u9898\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4e2d\u770b\u5230\u7684\u6982\u5ff5\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4ee5(-1.3)\u4e3a\u4e2d\u5fc3\u3001\u5b9e\u534a\u8f74\u957f\u5ea6\u4e3a3\u4e2a\u5355\u4f4d\u3001\u865a\u534a\u8f74(\u5e73\u884c\u4e8eY\u8f74)\u957f\u5ea6\u4e3a7\u4e2a\u5355\u4f4d\u7684\u53cc\u66f2\u7ebf\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\">\u8981\u627e\u5230\u53cc\u66f2\u7ebf\u65b9\u7a0b\uff0c\u53ea\u9700\u5e94\u7528\u53cc\u66f2\u7ebf\u5e38\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-2b3ab0b73fd88032017edcdc4c41fbdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x-x_0)^2}{a^2}-\\cfrac{(y-y_0)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"195\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u53cc\u66f2\u7ebf\u4e2d\u5fc3\u5750\u6807\u4ee3\u5165\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-cb8ad6c303104b76fdfe294488c60b30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x-(-1))^2}{a^2}-\\cfrac{(y-3)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"206\" style=\"vertical-align: -12px;\"><\/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-bd828d8d4d401a7179e88f283b89fb0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+1)^2}{a^2}-\\cfrac{(y-3)^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"179\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u66ff\u6362\u672a\u77e5\u6570\u7684\u503c<\/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>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586bc1b16791cf732fc00ee37db4357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" 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-fc9216ffda5e5a35c5349a4c0162f456_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(x+1)^2}{3^2}-\\cfrac{(y-3)^2}{7^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"179\" style=\"vertical-align: -12px;\"><\/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-3a6dc9e5e100bccc73644512fcac3344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\bm{(x+1)^2}}{\\bm{9}}\\bm{-}\\cfrac{\\bm{(y-3)^2}}{\\bm{49}} \\bm{= 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"166\" style=\"vertical-align: -12px;\"><\/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>\u6c42\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\u3001\u9876\u70b9\u3001\u7126\u70b9\u3001\u504f\u5fc3\u7387\u503c\u548c\u6e10\u8fd1\u7ebf\u7684\u5750\u6807\uff0c\u5176\u65b9\u7a0b\u5b9a\u4e49\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-024bdc18c959ac2ec840e7701edb4c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{25}-\\cfrac{y^2}{144} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"100\" style=\"vertical-align: -12px;\"><\/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\">\u9996\u5148\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u65b9\u7a0b\u4e2d\u7684\u8d1f\u53d8\u91cf\u662f\u53d8\u91cf<em>y<\/em> \uff0c\u56e0\u6b64\u53cc\u66f2\u7ebf\u7684\u5206\u652f\u5c06\u5411\u53f3\u548c\u5411\u5de6\u6253\u5f00\uff08\u7126\u8f74\u5e73\u884c\u4e8e X \u8f74\uff09\u3002<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u8be5\u65b9\u7a0b\u5bf9\u5e94\u4e8e\u53cc\u66f2\u7ebf\u7684\u6b63\u5219\uff08\u6216\u7b80\u5316\uff09\u65b9\u7a0b\uff0c\u56e0\u6b64\u5176\u4e2d\u5fc3\u662f\u5750\u6807\u539f\u70b9\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-6cc3df15d40bf714accb800d97cc619d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{O(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\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\uff0c\u4e3a\u4e86\u8ba1\u7b97\u5176\u4ed6\u6240\u6709\u5185\u5bb9\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u5b9e\u534a\u8f74\u7684\u503c\uff08\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-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>\uff09\u548c\u865a\u534a\u8f74\uff08\u53c2\u6570<\/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>\uff09\u3002\u6211\u4eec\u53ef\u4ee5\u4ece\u53cc\u66f2\u7ebf\u7684\u6b63\u5219\uff08\u6216\u7b80\u5316\uff09\u65b9\u7a0b\u7684\u516c\u5f0f\u4e2d\u63a8\u5bfc\u51fa\u4e24\u8005\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-c236b71767c0cd45cba2e3be0826c02c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{a^2}-\\cfrac{y^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"90\" style=\"vertical-align: -12px;\"><\/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-024bdc18c959ac2ec840e7701edb4c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{25}-\\cfrac{y^2}{144} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-99\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c686e5df986b42acb7cae3ffa7226636_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2 = 25\" 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-30e75133dba02b3a9db45660814d8a8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a = \\sqrt{25}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -2px;\"><\/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-05c584db6eed155346c907e19f10f11f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e82b959fd678557ff50e9c147f301b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b^2 = 144\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"66\" 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-8eb15c44c5845841e91b49a46c744c5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b= \\sqrt{144}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -2px;\"><\/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-517b154a5fe27c41ae6666be7858a2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b = 12\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5982\u679c\u4e2d\u5fc3\u548c\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a 5 \u4e2a\u5355\u4f4d\uff0c\u5219\u610f\u5473\u7740\u53cc\u66f2\u7ebf\u7684\u9876\u70b9\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-6a4fcc88007b1dd5424d647be5940951_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{A(-5,0) \\qquad A'(5,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8981\u786e\u5b9a\u6bcf\u4e2a\u7126\u70b9\u7684\u5750\u6807\uff0c\u5fc5\u987b\u77e5\u9053\u534a\u7126\u8ddd\u7684\u503c\uff08\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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff09\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fde\u63a5\u53cc\u66f2\u7ebf\u5143\u7d20\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-6d7a13f23d60337d2591c3d955d44faf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c^2 = a^2+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\"><\/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-44e92e889aa75e6513e84583d2e6b63f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c = \\sqrt{a^2+b^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -2px;\"><\/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-33e9779ed2710c2a5847aed0250c44de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c = \\sqrt{5^2+12^2} = \\sqrt{169} =13\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"216\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e2d\u5fc3\u548c\u4f4f\u5b85\u4e4b\u95f4\u6709 13 \u4e2a\u5355\u4f4d\u7684\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u6bcf\u6237\u7684\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-7e00737bd255cf07f0a2cc1439ee20fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{F(-13,0) \\qquad F'(13,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"177\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u90a3\u4e48\uff0c\u8981\u8ba1\u7b97\u53cc\u66f2\u7ebf\u7684\u504f\u5fc3\u7387\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5176\u76f8\u5e94\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-07e71b6f9c085cd16386db6dbfa535fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e= \\cfrac{c}{a} = \\cfrac{13}{5} = \\bm{2,6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u627e\u5230\u53cc\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf\u53ca\u5176\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-f40446ceecabf0eef8002b00c4573509_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{b}{a} x \\ \\longrightarrow \\ \\bm{y=}\\mathbf{\\cfrac{12}{5}}\\bm{ x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"165\" style=\"vertical-align: -12px;\"><\/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-4342ba83cc31ebbddfb3ec9af9cb1a81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -\\cfrac{b}{a}x \\ \\longrightarrow \\ \\bm{y=-}\\mathbf{\\cfrac{12}{5}}\\bm{ x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"198\" style=\"vertical-align: -12px;\"><\/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>\u5df2\u77e5\u53cc\u66f2\u7ebf\u4e0a\u4e00\u70b9\u5230\u7126\u70b9 F(-4.0) \u548c F(4.0) \u7684\u8ddd\u79bb\u5dee\u4e3a 6 \u4e2a\u5355\u4f4d\uff0c\u8ba1\u7b97\u4ee5\u5750\u6807\u539f\u70b9\u4e3a\u4e2d\u5fc3\u7684\u53cc\u66f2\u7ebf\u65b9\u7a0b\u3002 <\/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\">\u9996\u5148\uff0c\u7531\u4e8e\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\u4f4d\u4e8e\u5750\u6807\u539f\u70b9\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u89c4\u8303\u6216\u7b80\u5316\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-c236b71767c0cd45cba2e3be0826c02c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{a^2}-\\cfrac{y^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"90\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u90a3\u4e48\uff0c\u6839\u636e\u53cc\u66f2\u7ebf\u7684\u5b9a\u4e49\uff0c\u5b83\u7684\u4e00\u4e2a\u70b9\u5230\u7126\u70b9\u7684\u8ddd\u79bb\u5dee\u7684\u7edd\u5bf9\u503c\uff08\u5728\u672c\u4f8b\u4e2d\u4e3a 6\uff09\u5fc5\u987b\u7b49\u4e8e\u5b9e\u8f74\u7684\u957f\u5ea6\uff08<\/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-02baaffe4ddb6a44400eb7ba175e566c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> \uff09\u3002\u7136\u800c\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-08f25424560ca1e7449189d00268f0b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert d_1 - d_2 \\rvert = 2a\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" 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-c92fd32d1b9224d57070def8a33317cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6 = 2a\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-f7697991f6530286db135148771103bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{2} = a\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" style=\"vertical-align: -12px;\"><\/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-69c8e4eacfcdf3d15f0ab833a6f785b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3 = a\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u53cc\u66f2\u7ebf\u7684\u4e2d\u5fc3\u662f\u70b9(0,0)\uff0c\u7126\u70b9\u662f\u70b9(4,0)\u3002\u4f7f\u5f97\u5230\u4e24\u70b9\u7684\u8ddd\u79bb\uff08\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-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>) \u4e3a 4 \u4e2a\u5355\u4f4d\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-19e4bf3e3b4b653178b1bed74696bd59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c =4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u77e5\u9053\u53c2\u6570\u7684\u503c<\/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-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>\u53cc\u66f2\u7ebf\u76843\u4e2a\u7279\u5f81\u7cfb\u6570\u4e4b\u95f4\u7684\u6570\u5b66\u5173\u7cfb\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-6d7a13f23d60337d2591c3d955d44faf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c^2 = a^2+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\"><\/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-20f1823b7d594ff5ce46d7a3fa93d705_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b^2 = c^2-a^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"92\" 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-bf1c86f4503ca5f0a9f512fcd52694c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b = \\sqrt{c^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -2px;\"><\/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-0c9365659745d3a91bd4edb6f8aeed7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b= \\sqrt{4^2-3^2} = \\sqrt{16-9} =\\sqrt{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"235\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u53cc\u66f2\u7ebf\u7684\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-c236b71767c0cd45cba2e3be0826c02c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{a^2}-\\cfrac{y^2}{b^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"90\" style=\"vertical-align: -12px;\"><\/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-4dd94f2521da1a5f549dfacf1c499539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^2}{3^2}-\\cfrac{y^2}{\\left(\\sqrt{7}\\right)^2} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"121\" style=\"vertical-align: -24px;\"><\/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-8fbcb767276c1ec68bb1bfaa2af8d478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\bm{x^2}}{\\bm{9}}-\\cfrac{\\bm{y^2}}{\\bm{7}} \\bm{= 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u53cc\u66f2\u7ebf\u7684\u6240\u6709\u5185\u5bb9\uff1a\u5b83\u662f\u4ec0\u4e48\u3001\u5b83\u7684\u7279\u5f81\u5143\u7d20\u662f\u4ec0\u4e48\u3001\u5982\u4f55\u627e\u5230\u5b83\u7684\u65b9\u7a0b\u3001\u793a\u4f8b\u3001\u5df2\u89e3\u7b54\u7684\u7ec3\u4e60\u7b49\u3002  &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%85%ac%e5%bc%8f%e5%85%83%e7%b4%a0%e6%96%b9%e7%a8%8b%e7%a4%ba%e4%be%8b%e7%bb%83%e4%b9%a0%e5%b7%b2%e8%a7%a3%e5%86%b3\/\"> <span class=\"screen-reader-text\">\u5938\u5f20\uff1a\u5b9a\u4e49\u3001\u516c\u5f0f\u3001\u5143\u7d20\u3001\u65b9\u7a0b\u5f0f\u3001\u793a\u4f8b\u2026\u2026<\/span> \u67e5\u770b\u5168\u6587 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