{"id":238,"date":"2023-07-10T18:34:04","date_gmt":"2023-07-10T18:34:04","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d1%8d%d0%bb%d0%bb%d0%b8%d0%bf%d1%81%d0%b0-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0\/"},"modified":"2023-07-10T18:34:04","modified_gmt":"2023-07-10T18:34:04","slug":"%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d1%8d%d0%bb%d0%bb%d0%b8%d0%bf%d1%81%d0%b0-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d1%8d%d0%bb%d0%bb%d0%b8%d0%bf%d1%81%d0%b0-%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0\/","title":{"rendered":"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430) \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u0438\u043c\u0435\u0435\u0442 \u043b\u0438 \u043e\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0432 \u0446\u0435\u043d\u0442\u0440\u0435 \u0438\u043b\u0438 \u043d\u0435\u0442. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043a\u0430\u043a \u0438\u0445 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0438 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u043e\u043d\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u044d\u043b\u043b\u0438\u043f\u0441\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-de-la-elipse\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430 <span class=\"ez-toc-section-end\"><\/span><\/h2>\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\"> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 <strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430<\/strong> \u0432 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0445:<\/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-e29350c8a9f9271d7c58bb5636661eae_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\"> \u0417\u043e\u043b\u043e\u0442\u043e:<\/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> \u0418<\/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> \u2013 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0446\u0435\u043d\u0442\u0440\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a54160c9f13bae428a2471d905abd6f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(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> \u2014 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0434\u0438\u0443\u0441 \u044d\u043b\u043b\u0438\u043f\u0441\u0430.<\/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> &#8212; \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0434\u0438\u0443\u0441 \u044d\u043b\u043b\u0438\u043f\u0441\u0430. <\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-dune-ellipse.webp\" alt=\"\u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430\" class=\"wp-image-2080\" width=\"408\" height=\"384\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-la-elipse-centrada-en-el-origen\"><\/span> \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041e\u0447\u0435\u043d\u044c \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u0439 \u0442\u0438\u043f \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u2014 \u044d\u0442\u043e \u0442\u043e\u0442, \u0446\u0435\u043d\u0442\u0440 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442, \u0442\u043e \u0435\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435 (0,0). \u0412\u043e\u0442 \u043f\u043e\u0447\u0435\u043c\u0443 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442.<\/p>\n<p> \u0421\u043b\u0435\u0434\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430:<\/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-e29350c8a9f9271d7c58bb5636661eae_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> \u0415\u0441\u043b\u0438 \u044d\u043b\u043b\u0438\u043f\u0441 \u0446\u0435\u043d\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u043d \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e<\/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> \u0418<\/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> \u0440\u0430\u0432\u043d\u044b 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0430\u0448\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442:<\/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-7821573c61c10361101554eb56041901_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\bm{x^2}}{\\bm{a^2}}+\\cfrac{\\bm{y^2}}{\\bm{b^2}} \\bm{= 1}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u041d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u044d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u0438\u043b\u0438 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u044d\u043b\u043b\u0438\u043f\u0441\u0430.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"elementos-de-la-elipse\"><\/span> \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a\u043e\u0432\u044b \u0435\u0433\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b. \u041d\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u044d\u043b\u043b\u0438\u043f\u0441:<\/p>\n<p> \u042d\u043b\u043b\u0438\u043f\u0441 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u0443\u044e \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u0443\u044e \u0438\u0437\u043e\u0433\u043d\u0443\u0442\u0443\u044e \u043b\u0438\u043d\u0438\u044e, \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0443\u044e \u043d\u0430 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c, \u043d\u043e \u043f\u043e \u0444\u043e\u0440\u043c\u0435 \u0431\u043e\u043b\u0435\u0435 \u043e\u0432\u0430\u043b\u044c\u043d\u0443\u044e. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u044d\u043b\u043b\u0438\u043f\u0441 \u2014 \u044d\u0442\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043c\u0435\u0441\u0442\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u0435\u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0441\u0443\u043c\u043c\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0434\u043e \u0434\u0432\u0443\u0445 \u0434\u0440\u0443\u0433\u0438\u0445 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a (\u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0445 \u0444\u043e\u043a\u0443\u0441\u0430\u043c\u0438 F \u0438 F&#8217;) \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430.<\/p>\n<p> \u0418\u0442\u0430\u043a, \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f:<\/p>\n<ul>\n<li> <strong>\u0424\u043e\u043a\u0443\u0441\u044b<\/strong> : \u044d\u0442\u043e \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 F \u0438 F&#8217; (\u0442\u043e\u0447\u043a\u0438 \u0444\u0438\u043e\u043b\u0435\u0442\u043e\u0432\u043e\u0433\u043e \u0446\u0432\u0435\u0442\u0430 \u043d\u0430 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0438 \u043d\u0438\u0436\u0435). \u0421\u0443\u043c\u043c\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043c\u0435\u0436\u0434\u0443 \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u043e\u0439 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0438 \u043a\u0430\u0436\u0434\u044b\u043c \u0444\u043e\u043a\u0443\u0441\u043e\u043c \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u0435\u043a \u044d\u043b\u043b\u0438\u043f\u0441\u0430.<\/li>\n<li> <strong>\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0438\u043b\u0438 \u0444\u043e\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u043e\u0441\u044c<\/strong> : \u044d\u0442\u043e \u043e\u0441\u044c \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u044b \u0444\u043e\u043a\u0443\u0441\u044b. \u0422\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0433\u043b\u0430\u0432\u043d\u043e\u0439 \u043e\u0441\u044c\u044e.<\/li>\n<li> <strong>\u0412\u0442\u043e\u0440\u0438\u0447\u043d\u0430\u044f \u043e\u0441\u044c<\/strong> : \u044d\u0442\u043e \u043e\u0441\u044c \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430\u044f \u0433\u043b\u0430\u0432\u043d\u043e\u0439 \u043e\u0441\u0438. \u0415\u0435 \u0435\u0449\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043c\u0430\u043b\u043e\u0439 \u043e\u0441\u044c\u044e \u0438 \u043e\u043d\u0430 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0431\u0438\u0441\u0441\u0435\u043a\u0442\u0440\u0438\u0441\u0435 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u0430, \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0449\u0435\u0433\u043e \u0444\u043e\u043a\u0443\u0441\u044b.<\/li>\n<li> <strong>\u0426\u0435\u043d\u0442\u0440<\/strong> : \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043e\u0441\u0435\u0439 \u044d\u043b\u043b\u0438\u043f\u0441\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u044d\u0442\u043e \u0446\u0435\u043d\u0442\u0440 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 (\u043e\u0440\u0430\u043d\u0436\u0435\u0432\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435).<\/li>\n<li> <strong>\u0412\u0435\u0440\u0448\u0438\u043d\u044b<\/strong> : \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u0435\u0433\u043e \u043e\u0441\u044f\u043c\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 (\u0447\u0435\u0440\u043d\u044b\u0435 \u0442\u043e\u0447\u043a\u0438).<\/li>\n<li> <strong>\u0411\u043e\u043b\u044c\u0448\u0430\u044f \u043f\u043e\u043b\u0443\u043e\u0441\u044c \u0438\u043b\u0438 \u0433\u043b\u0430\u0432\u043d\u0430\u044f \u043e\u0441\u044c:<\/strong> \u043e\u0442\u0440\u0435\u0437\u043e\u043a, \u0438\u0434\u0443\u0449\u0438\u0439 \u043e\u0442 \u0446\u0435\u043d\u0442\u0440\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u043a \u0432\u0435\u0440\u0448\u0438\u043d\u0430\u043c \u0433\u043b\u0430\u0432\u043d\u043e\u0439 \u043e\u0441\u0438.<\/li>\n<li> <strong>\u041c\u0430\u043b\u0430\u044f \u043f\u043e\u043b\u0443\u043e\u0441\u044c \u0438\u043b\u0438 \u0432\u0442\u043e\u0440\u0438\u0447\u043d\u0430\u044f \u043e\u0441\u044c:<\/strong> \u0441\u0435\u0433\u043c\u0435\u043d\u0442 \u043c\u0435\u0436\u0434\u0443 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0438 \u0432\u0435\u0440\u0448\u0438\u043d\u0430\u043c\u0438 \u0432\u0442\u043e\u0440\u0438\u0447\u043d\u043e\u0439 \u043e\u0441\u0438.<\/li>\n<li> <strong>\u0424\u043e\u043a\u0443\u0441\u043d\u043e\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435<\/strong> : \u044d\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0444\u043e\u043a\u0443\u0441\u043d\u044b\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438.<\/li>\n<li> <strong>\u041f\u043e\u043b\u0443\u0444\u043e\u043a\u0443\u0441\u043d\u043e\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435<\/strong> : \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043c\u0435\u0436\u0434\u0443 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0438 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0437 \u0444\u043e\u043a\u0443\u0441\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a.<\/li>\n<li> <strong>\u0420\u0430\u0434\u0438\u043e\u0432\u0435\u043a\u0442\u043e\u0440\u044b<\/strong> : \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0442 \u043b\u044e\u0431\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u0444\u043e\u043a\u0443\u0441\u043e\u043c (\u0441\u0438\u043d\u0438\u0435 \u0441\u0435\u0433\u043c\u0435\u043d\u0442\u044b \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435). <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/elements-dellipse.webp\" alt=\"\u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430\" class=\"wp-image-2082\" width=\"581\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relacion-entre-los-elementos-de-una-elipse\"><\/span> \u0421\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0420\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0441\u0432\u044f\u0437\u0438 \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438 \u043e\u0447\u0435\u043d\u044c \u0432\u0430\u0436\u043d\u044b \u0434\u043b\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\u0445, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\u0445 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439.<\/p>\n<p class=\"has-text-align-left\"> \u041a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432\u044b\u0448\u0435 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0434\u043e \u0444\u043e\u043a\u0443\u0441\u0430 F \u043f\u043b\u044e\u0441 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u0444\u043e\u043a\u0443\u0441\u0430 F&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u043c. \u0427\u0442\u043e \u0436, \u044d\u0442\u043e \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432 \u0434\u0432\u0430 \u0440\u0430\u0437\u0430 \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c \u0438\u0437\u043c\u0435\u0440\u044f\u0435\u0442 \u0431\u043e\u043b\u044c\u0448\u0430\u044f \u043f\u043e\u043b\u0443\u043e\u0441\u044c. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e:<\/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-7cef5996a2621318273bd54d01594941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,F) + d(P,F')= 2a\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0417\u043e\u043b\u043e\u0442\u043e<\/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-6be809958050006a77cc59c5b7c32557_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,F)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52cd58325f7f5f8ae50bf05b32b7ed55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,F')\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p> &#8212; \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 P \u0434\u043e \u0444\u043e\u043a\u0443\u0441\u0430 F \u0438 F&#8217; \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0438<\/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> \u2013 \u0434\u043b\u0438\u043d\u0430 \u043f\u043e\u043b\u0443\u0444\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u0441\u0438.<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u0435\u0440\u0448\u0438\u043d\u0430 \u0432\u0442\u043e\u0440\u0438\u0447\u043d\u043e\u0439 \u043e\u0441\u0438 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043a\u0430\u043a \u0440\u0430\u0437 \u043f\u043e\u0441\u0435\u0440\u0435\u0434\u0438\u043d\u0435 \u0444\u043e\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u0441\u0438, \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043d\u0435\u0435 \u0434\u043e \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437 \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0434\u043b\u0438\u043d\u0435 \u043f\u043e\u043b\u0443\u043f\u0435\u0440\u0432\u0438\u0447\u043d\u043e\u0439 \u043e\u0441\u0438 (<\/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> ): <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/relation-delements-dellipse.webp\" alt=\"\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\" class=\"wp-image-2087\" width=\"332\" height=\"197\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438\u0437  \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430  \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 <strong>\u0441\u0432\u044f\u0437\u044c, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u043c\u0435\u0436\u0434\u0443 \u0433\u043b\u0430\u0432\u043d\u043e\u0439 \u043f\u043e\u043b\u0443\u043e\u0441\u044c\u044e, \u0432\u0442\u043e\u0440\u0438\u0447\u043d\u043e\u0439 \u043f\u043e\u043b\u0443\u043e\u0441\u044c\u044e \u0438 \u043f\u043e\u043b\u0443\u0444\u043e\u043a\u0443\u0441\u043d\u044b\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435\u043c:<\/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-f07be3767557be2f8c17fc9a226a2506_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2=b^2+c^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> \u0417\u0430\u043f\u043e\u043c\u043d\u0438\u0442\u0435 \u044d\u0442\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u043b\u0435\u0437\u043d\u0430 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\u043c\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"excentricidad-de-la-elipse\"><\/span> \u042d\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442 \u044d\u043b\u043b\u0438\u043f\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u043d\u0435 \u0432\u0441\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u044b \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b, \u043d\u043e \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0431\u043e\u043b\u0435\u0435 \u0432\u044b\u0442\u044f\u043d\u0443\u0442\u044b, \u0430 \u0434\u0440\u0443\u0433\u0438\u0435 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u0438\u043f\u043b\u044e\u0441\u043d\u0443\u0442\u044b. \u0418\u0442\u0430\u043a, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f \u0442\u043e\u0433\u043e, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043e\u043a\u0440\u0443\u0433\u043b\u0435\u043d \u0434\u0430\u043d\u043d\u044b\u0439 \u044d\u043b\u043b\u0438\u043f\u0441. \u042d\u0442\u043e\u0442 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u044d\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442\u043e\u043c<\/strong> \u0438 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/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-01e68e598b53e74e9420afdb1bf6ab66_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> \u0417\u043e\u043b\u043e\u0442\u043e<\/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> \u2014 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0446\u0435\u043d\u0442\u0440\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0434\u043e \u043e\u0434\u043d\u043e\u0433\u043e \u0438\u0437 \u0435\u0433\u043e \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u0438<\/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> \u0434\u043b\u0438\u043d\u0430 \u0431\u043e\u043b\u044c\u0448\u043e\u0439 \u043f\u043e\u043b\u0443\u043e\u0441\u0438. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/excentricite-dellipse.webp\" alt=\"\u044d\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\" class=\"wp-image-2095\" width=\"669\" height=\"154\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u043d\u043e \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0438, \u0447\u0435\u043c \u043c\u0435\u043d\u044c\u0448\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u044d\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u0442\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043e\u043d \u043d\u0430\u043f\u043e\u043c\u0438\u043d\u0430\u0435\u0442 \u043a\u0440\u0443\u0433, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0447\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442, \u0442\u0435\u043c \u0431\u043e\u043b\u0435\u0435 \u0441\u043f\u043b\u044e\u0449\u0435\u043d\u043d\u044b\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u044d\u043b\u043b\u0438\u043f\u0441. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u044d\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442\u0430 \u0432\u0430\u0440\u044c\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u043e\u0442 \u043d\u0443\u043b\u044f (\u0438\u0434\u0435\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u0440\u0443\u0433) \u0434\u043e \u0435\u0434\u0438\u043d\u0438\u0446\u044b (\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u043b\u0438\u043d\u0438\u044f), \u043d\u0435 \u0432\u043a\u043b\u044e\u0447\u0430\u044f \u043e\u0431\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430.<\/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-d7cba3912f2e788be4e73f1e18c9fb21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0\n\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;ejemplo-de-como-calcular-la-ecuacion-de-la-elipse&quot;><\/span> Exemple de calcul de l&#8217;\u00e9quation de l&#8217;ellipse<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> Une fois que nous avons vu toutes les propri\u00e9t\u00e9s de l&#8217;ellipse, nous allons r\u00e9soudre un probl\u00e8me d&#8217;ellipse \u00e0 titre d&#8217;exemple :<\/p>\n<ul>\n<li> Trouver l&#8217;\u00e9quation de l&#8217;ellipse dont le demi-axe principal mesure 5 unit\u00e9s (et est parall\u00e8le \u00e0 l&#8217;axe OX), son centre est le point C(4,-1) et la distance de son centre \u00e0 un foyer est de 4 unit\u00e9s.<\/li>\n<\/ul>\n<p> <strong>Pour d\u00e9terminer l&#8217;\u00e9quation d&#8217;une ellipse, nous avons besoin de la longueur du demi-axe principal, de la longueur du demi-axe secondaire et des coordonn\u00e9es de son point.<\/strong> Par cons\u00e9quent, dans ce cas, nous n&#8217;avons besoin de conna\u00eetre que l&#8217;axe semi-secondaire. Ainsi, pour calculer la longueur mesur\u00e9e par l&#8217;axe semi-secondaire, nous pouvons utiliser la relation entre l&#8217;axe semi-principal, l&#8217;axe semi-secondaire et la distance semi-focale : &#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;215&#8243; width=&#187;2133&#8243; style=&#187;vertical-align: -5px;&#187;><\/p>\n<p> a^2=b^2+c^2 b^2=a^2-c^2 b=\\sqrt{a^2-c^2} = \\sqrt{5^2-4^2}=\\sqrt {9} = 3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ac0d898ef827d924f8a7972d18a3d37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Et une fois que l'on conna\u00eet la longueur des deux demi-axes et son centre, on peut trouver l'\u00e9quation de l'ellipse \u00e0 l'aide de sa formule : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"977\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-4)^2}{5^2 }+\\cfrac{(y-(-1))^2}{3^2} = 1\\cfrac{\\bm{(x-4)^2}}{\\bm{25}}+\\cfrac{\\ \u0431\u043c{(y+1)^2}}{\\bm{9}} \\bm{= 1}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c8518a77b08b28dd3989532a9c1a0bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;ejercicios-resueltos-de-la-ecuacion-de-la-elipse&quot;><\/span> Probl\u00e8mes r\u00e9solus de l&#8217;\u00e9quation de l&#8217;ellipse<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<h3 class=&quot;wp-block-heading&quot;> Exercice 1<\/h3>\n<p> Quelle est l&#8217;\u00e9quation de l&#8217;ellipse centr\u00e9e au point C(2,0) dont l&#8217;axe semi-principal (parall\u00e8le \u00e0 l&#8217;axe X) et l&#8217;axe secondaire mesurent respectivement 6 et 3 unit\u00e9s ? Repr\u00e9senter graphiquement ladite ellipse. <\/p>\n<div class=&quot;wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE&quot; role=&quot;button&quot; tabindex=&quot;0&quot; aria-expanded=&quot;false&quot; data-otfm-spc=&quot;#E4F0FE&quot; style=&quot;text-align:center&quot;>\n<div class=&quot;otfm-sp__title&quot;> <strong>voir solution<\/strong><\/div>\n<\/div>\n<p> L&#8217;\u00e9quation de l&#8217;ellipse est la suivante :&#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;208&#8243; width=&#187;1595&#8243; style=&#187;vertical-align: -20px;&#187;><\/p>\n<p> \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a535f3c26d0c91d21ff2802c71cb131_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Par cons\u00e9quent, \u00e0 partir des donn\u00e9es de l'\u00e9nonc\u00e9, nous pouvons compl\u00e9ter l'\u00e9quation de l'ellipse : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"709\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\cfrac{(x-2)^2}{6^2}+\\cfrac{(y-0)^2}{3^2} = 1\\cfrac{\\bm{(x-2)^2}} {\\bm{36}}+\\cfrac{\\bm{y^2}}{\\bm{9}} \\bm{= 1}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e674e398f6c61cceb56ebc7d6849b2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Et une fois que nous connaissons l'\u00e9quation de l'ellipse, nous pouvons tracer la figure : \n\n<div class=&quot;wp-block-image&quot;>\n<figure class=&quot;aligncenter size-large is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/centre-de-lellipse-de-lequation-a-lexterieur-de-lorigine.webp&quot; alt=&quot;\u00e9quation de l'ellipse avec le centre hors de l'origine&quot; class=&quot;wp-image-2106&quot; width=&quot;524&quot; height=&quot;368&quot; srcset=&quot;&quot; sizes=&quot;&quot;><\/figure>\n<\/div>\n<div class=&quot;wp-block-otfm-box-spoiler-end otfm-sp_end&quot;><\/div>\n<h3 class=&quot;wp-block-heading&quot;> Exercice 2<\/h3>\n<p> Calculer l&#8217;\u00e9quation de l&#8217;ellipse dont le demi-axe principal (parall\u00e8le \u00e0 l&#8217;axe des abscisses) mesure 13 unit\u00e9s, son centre est l&#8217;origine des coordonn\u00e9es et la distance de son centre \u00e0 l&#8217;un de ses foyers est de 5 unit\u00e9s. <\/p>\n<div class=&quot;wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE&quot; role=&quot;button&quot; tabindex=&quot;0&quot; aria-expanded=&quot;false&quot; data-otfm-spc=&quot;#E4F0FE&quot; style=&quot;text-align:center&quot;>\n<div class=&quot;otfm-sp__title&quot;> <strong>voir solution<\/strong><\/div>\n<\/div>\n<p> Pour calculer l&#8217;\u00e9quation de l&#8217;ellipse, nous devons savoir combien de temps mesure l&#8217;axe semi-secondaire. Et, pour cela, on peut utiliser la relation math\u00e9matique qui existe entre le demi-axe principal, le demi-axe secondaire et la demi-distance focale : &#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;299&#8243; width=&#187;2688&#8243; style=&#187;vertical-align: -20px;&#187;><\/p>\n<p> a^2=b^2+c^2 b^2=a^2-c^2 b=\\sqrt{a^2-c^2} = \\sqrt{13^2-5^2}=\\sqrt {144} = 12<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bcf056c99846b69f1bf4ed5ce1e6552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Et une fois que l'on conna\u00eet la longueur des deux demi-axes et son centre, on peut trouver l'\u00e9quation de l'ellipse gr\u00e2ce \u00e0 sa formule : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"960\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-0)^2}{13^2 }+\\cfrac{(y-0)^2}{12^2} = 1\\cfrac{\\bm{x^2}}{\\bm{169}}+\\cfrac{\\bm{y^2}} {\\bm{144}} \\bm{= 1}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e53a75087af9221fe85fa404a4045ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;wp-block-otfm-box-spoiler-end otfm-sp_end&quot;><\/div>\n<h3 class=&quot;wp-block-heading&quot;> Exercice 3<\/h3>\n<p> D\u00e9terminer l&#8217;\u00e9quation de l&#8217;ellipse suivante et les coordonn\u00e9es de ses foyers : <\/p>\n<div class=&quot;wp-block-image&quot;>\n<figure class=&quot;aligncenter size-large is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-de-lequation-de-lellipse.webp&quot; alt=&quot;exercices r\u00e9solus pas \u00e0 pas d'\u00e9quations d'ellipses&quot; class=&quot;wp-image-2111&quot; width=&quot;533&quot; height=&quot;404&quot; srcset=&quot;&quot; sizes=&quot;&quot;><\/figure>\n<\/div>\n<div class=&quot;wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE&quot; role=&quot;button&quot; tabindex=&quot;0&quot; aria-expanded=&quot;false&quot; data-otfm-spc=&quot;#E4F0FE&quot; style=&quot;text-align:center&quot;>\n<div class=&quot;otfm-sp__title&quot;> <strong>voir solution<\/strong><\/div>\n<\/div>\n<p> Les sommets horizontaux de l&#8217;ellipse sont les points (-4,1) et (10,1). Par cons\u00e9quent, son diam\u00e8tre horizontal et son rayon sont : &#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;252&#8243; width=&#187;2047&#8243; style=&#187;vertical-align: -20px;&#187;><\/p>\n<p> d_h=10-(-4) =14 a =\\cfrac{14}{2} = 7<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-76aa999f562c86113192c06e01991927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" De m\u00eame, les sommets verticaux de l'ellipse sont les points (3,6) et (3,-4). Par cons\u00e9quent, son diam\u00e8tre vertical et son rayon sont : \" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"963\" style=\"vertical-align: -5px;\"><\/p>\n<p> d_v=6-(-4) =10 b =\\cfrac{10}{2} = 5<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ac099c741c43ec962a36c7b2bba5d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Il suffit donc de trouver les coordonn\u00e9es du centre de l'ellipse, qui correspondent aux milieux des extr\u00e9mit\u00e9s de l'ellipse : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"884\" style=\"vertical-align: -4px;\"><\/p>\n<p> C_x= \\cfrac{10+(-4)}{2} = \\cfrac{6}{2} =3 C_y=&nbsp;\\cfrac{6+(-4)}{2} = \\cfrac{2}{ 2} = 1 \u0421(3.1)<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-51217c6f75e2ad233a651376f2ded0e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Enfin, l'\u00e9quation de l'ellipse est : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"249\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-3)^2}{7^2 }+\\cfrac{(y-1)^2}{5^2} =1\\cfrac{\\bm{(x-3)^2}}{\\bm{49}}+\\cfrac{\\bm{( y-1)^2}}{\\bm{25}} \\bm{= 1}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-310ed81b139fc6b5d3902b75bed66c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, la distance semi-focale vaut : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"339\" style=\"vertical-align: -4px;\"><\/p>\n<p> a^2=b^2+c^2 c^2=a^2-b^2 c=\\sqrt{a^2-b^2} = \\sqrt{7^2-5^2}=\\sqrt {24}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1653b114c298901c587b9af56e4b0c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Cela signifie que les foyers de l'ellipse sont situ\u00e9s \u00e0 une distance horizontale de\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"578\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\sqrt{24}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f5155fae442053fd60dec7ee847fe0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"unit\u00e9s du centre de l'ellipse, donc les coordonn\u00e9es des foyers sont : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"483\" style=\"vertical-align: -4px;\"><\/p>\n<p> C(3,1) \\bm{F\\left(3+\\sqrt{24},1}\\right)} \\bm{F\\left(3-\\sqrt{24},1}\\right)}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d494da27f7cde61e219586567d178c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;wp-block-otfm-box-spoiler-end otfm-sp_end&quot;><\/div>\n<h3 class=&quot;wp-block-heading&quot;> Exercice 4<\/h3>\n<p> Calculez l&#8217;\u00e9quation de l&#8217;ellipse qui r\u00e9pond aux caract\u00e9ristiques suivantes :<\/p>\n<ul>\n<li> Son centre est l&#8217;origine des coordonn\u00e9es du plan cart\u00e9sien.<\/li>\n<li> Sa distance focale est \u00e9gale \u00e0 6 unit\u00e9s.<\/li>\n<li> Un point de l&#8217;ellipse est \u00e0 3 et 5 unit\u00e9s de ses foyers. <\/li>\n<\/ul>\n<div class=&quot;wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE&quot; role=&quot;button&quot; tabindex=&quot;0&quot; aria-expanded=&quot;false&quot; data-otfm-spc=&quot;#E4F0FE&quot; style=&quot;text-align:center&quot;>\n<div class=&quot;otfm-sp__title&quot;> <strong>voir solution<\/strong><\/div>\n<\/div>\n<p> On peut calculer la demi-focale \u00e0 partir de la focale : &#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;185&#8243; width=&#187;1667&#8243; style=&#187;vertical-align: -19px;&#187;><\/p>\n<p> 2c = 6 c=\\cfrac{6}{2} c=3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae016b9237aee40e4130230eb495fe6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, on sait par la d\u00e9finition de l'ellipse que la somme des distances de chacun de ses points \u00e0 ses foyers est \u00e9quivalente \u00e0 la longueur de son axe principal, donc : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1214\" style=\"vertical-align: -4px;\"><\/p>\n<p> d(P,F) + d(P,F&#8217;)= 2a 3+5= 2a 8= 2a \\cfrac{8}{2}= a 4= a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-615d5b2ccb4a343777d9d707806526ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Par cons\u00e9quent, la longueur du demi-axe secondaire de l'ellipse vaut : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"529\" style=\"vertical-align: -4px;\"><\/p>\n<p> a^2=b^2+c^2 b^2=a^2-c^2 b=\\sqrt{a^2-c^2} = \\sqrt{4^2-3^2}=\\sqrt {7}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-98a1c514fb7344ec3be2558c5a559feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Et, en conclusion, l'\u00e9quation de l'ellipse est : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"328\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\cfrac{(x-x_0)^2}{a^2}+\\cfrac{(y-y_0)^2}{b^2} = 1\\cfrac{(x-0)^2}{4^2 }+\\cfrac{(y-0)^2}{\\left(\\sqrt{7}\\right)^2} =1\\cfrac{\\bm{x^2}}{\\bm{16}}+\\ cfrac{\\bm{y^2}}{\\bm{7}} \\bm{= 1}$<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0435\u0441\u043b\u0438 \u044d\u0442\u0430 \u0441\u0442\u0430\u0442\u044c\u044f \u0431\u044b\u043b\u0430 \u0432\u0430\u043c \u043f\u043e\u043b\u0435\u0437\u043d\u0430, \u0432\u0430\u0441 \u043d\u0430\u0432\u0435\u0440\u043d\u044f\u043a\u0430 \u0437\u0430\u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u044e\u0442 \u0438 \u043d\u0430\u0448\u0438 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b, \u043f\u043e\u0441\u0432\u044f\u0449\u0435\u043d\u043d\u044b\u0435  \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b  \u0438  \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b  . \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430 \u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430, \u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0438\u0445 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f,\u2026<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430) \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u0438\u043c\u0435\u0435\u0442 \u043b\u0438 \u043e\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0432 \u0446\u0435\u043d\u0442\u0440\u0435 \u0438\u043b\u0438 \u043d\u0435\u0442. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430, \u043a\u0430\u043a \u0438\u0445 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0438 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u043e\u043d\u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 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