{"id":28997,"date":"2021-05-05T13:00:09","date_gmt":"2021-05-05T13:00:09","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28997"},"modified":"2024-09-22T01:55:07","modified_gmt":"2024-09-22T01:55:07","slug":"%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb-%d0%b8-%d0%b5%d0%b3%d0%be-%d0%b2%d1%8b%d0%b2%d0%be%d0%b4","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb-%d0%b8-%d0%b5%d0%b3%d0%be-%d0%b2%d1%8b%d0%b2%d0%be%d0%b4\/","title":{"rendered":"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0432\u044b\u0432\u043e\u0434"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0432\u044b\u0432\u043e\u0434<\/h1>\n<p><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n\u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0441\u0440\u0430\u0432\u043d\u0438\u043c \u0435\u0451 \u0441 \u044d\u043b\u043b\u0438\u043f\u0441\u043e\u043c \u0438 \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u043e\u0431\u0449\u0435\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<br \/>\n   <\/em><\/p>\n<p>   <strong>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:<\/strong><br \/>\n   \u041a \u043a\u043e\u043d\u0446\u0443 \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u0441\u043c\u043e\u0433\u0443\u0442:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c<\/strong>, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430.<\/li>\n<li><strong>\u0412\u044b\u0432\u0435\u0441\u0442\u0438<\/strong> \u043e\u0431\u0449\u0435\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0438\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u0435\u0451 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/li>\n<li><strong>\u0412\u044b\u044f\u0432\u0438\u0442\u044c<\/strong> \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\u043c\u0438 \u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430\u043c\u0438 \u0441 \u0442\u043e\u0447\u043a\u0438 \u0437\u0440\u0435\u043d\u0438\u044f \u0444\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439.<\/li>\n<\/ol>\n<p>   <strong>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><br \/>\n<a href=\"#1\">\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/a><br \/>\n<a href=\"#2\">\u0412\u044b\u0432\u043e\u0434 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/a><br \/>\n<a href=\"#3\">\u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/a><br \/>\n<a href=\"#4\">\u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/a>\n   <\/p>\n<p>   <\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/1Aearz-E3bk\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a>   <\/p>\n<h2>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/h2>\n<p style=\"text-align: justify;\">\u0420\u0430\u043d\u0435\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u043e\u0432 \u0438 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u0432\u044b\u044f\u0441\u043d\u0438\u043b\u0438, \u0447\u0442\u043e \u043e\u043d\u0438 \u0438\u043c\u0435\u044e\u0442 \u0432\u0438\u0434 <span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + cy^2 + dy + e = 0<\/span>, \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u2014 \u044d\u0442\u043e \u0434\u0432\u0430 \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u044b\u0445 \u0447\u0438\u0441\u043b\u0430 \u0441 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u043c\u0438 \u0437\u043d\u0430\u043a\u0430\u043c\u0438. \u041c\u044b \u043e\u0442\u043c\u0435\u0442\u0438\u043b\u0438, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0438\u043c\u0435\u044e\u0442 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0435 \u0437\u043d\u0430\u043a\u0438, \u0442\u043e \u0432\u043c\u0435\u0441\u0442\u043e \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430. \u041c\u044b \u043d\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u043b\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 \u043e \u044d\u0442\u0438\u0445 \u043a\u0440\u0438\u0432\u044b\u0445, \u043d\u043e \u0441\u0435\u0439\u0447\u0430\u0441 \u0432\u043e\u0441\u043f\u043e\u043b\u043d\u0438\u043c \u044d\u0442\u043e\u0442 \u043f\u0440\u043e\u0431\u0435\u043b. \u041c\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0443 \u0441 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0437\u0440\u0435\u043d\u0438\u044f \u0438 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0435\u0451 \u043e\u0431\u0449\u0435\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=176s\" target=\"_blank\" rel=\"noopener\"><strong>\u042d\u043b\u043b\u0438\u043f\u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f<\/strong><\/a> \u043a\u0430\u043a \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u0435\u043a, \u0442\u0430\u043a\u0438\u0445 \u0447\u0442\u043e \u0441\u0443\u043c\u043c\u0430 \u0438\u0445 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u0434\u043e \u0434\u0432\u0443\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, \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430 \u2014 \u044d\u0442\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0442\u043e\u0447\u0435\u043a, \u0442\u0430\u043a\u0438\u0445 \u0447\u0442\u043e \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u0438\u0445 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u043c.<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-BNQiwaq_OJs\/YJGda6VHOmI\/AAAAAAAAFDo\/edTQHWwLGGQwyGszR7c-7H74a09ASsK2gCLcBGAsYHQ\/s0\/hiperbola%2Bdefinici%25C3%25B3n%2Bgr%25C3%25A1fica.PNG\" alt=\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b\" class=\" aligncenter lazyload\" width=\"493\" height=\"340\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-BNQiwaq_OJs\/YJGda6VHOmI\/AAAAAAAAFDo\/edTQHWwLGGQwyGszR7c-7H74a09ASsK2gCLcBGAsYHQ\/s0\/hiperbola%2Bdefinici%25C3%25B3n%2Bgr%25C3%25A1fica.PNG\" alt=\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b\" class=\" aligncenter lazyload\" width=\"493\" height=\"340\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0418\u043d\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">|d(f_1,P) - d(f_2,P)| = 2a<\/span>\n<p style=\"text-align: justify;\">\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u2014 \u044d\u0442\u043e \u043b\u044e\u0431\u043e\u0435 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e.<\/p>\n<p style=\"text-align: justify;\">\u042d\u0442\u043e \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0434\u0432\u0443\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c: <span class=\"katex-eq\" data-katex-display=\"false\">d(f_1,P) - d(f_2,P) = 2a<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">d(f_2,P) - d(f_1,P) = 2a<\/span>, \u043a\u0430\u0436\u0434\u043e\u0435 \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043e\u0434\u043d\u0443 \u0438\u0437 \u0432\u0435\u0442\u0432\u0435\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b.<\/p>\n<p><a name=\"2\"><\/a>  <\/p>\n<h2>\u0412\u044b\u0432\u043e\u0434 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=331s\" target=\"_blank\" rel=\"noopener\"><strong>\u0418\u0437 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438<\/strong><\/a> \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043d\u0430\u0447\u043d\u0435\u043c \u0441 \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0435\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f \u0438 \u043e\u0442\u0442\u0443\u0434\u0430 \u043f\u0435\u0440\u0435\u0439\u0434\u0451\u043c \u043a \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f\u043c. \u041d\u0430\u0448\u0435 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u043e \u043a \u043e\u0434\u043d\u043e\u0439 \u0432\u0435\u0442\u0432\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0434\u0440\u0443\u0433\u0443\u044e \u0432\u0435\u0442\u0432\u044c.<\/p>\n<h3>\u0412\u044b\u0432\u043e\u0434 \u0443\u043f\u0440\u043e\u0449\u0451\u043d\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u044b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=356s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0430 \u0444\u043e\u043a\u0443\u0441\u0430<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f_1 = (-c,0)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f_2 = (c,0).<\/span> \u0422\u043e\u0447\u043a\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">p = (x,y)<\/span> \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043d\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0435, \u0435\u0441\u043b\u0438<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-SMOUgyC1lM4\/YJGg_MIkJTI\/AAAAAAAAFDw\/6JzXOcfZi70lpvTZtbC6y26AvTQzcnWNgCLcBGAsYHQ\/s0\/hiperbola%2Bcentrada%2Ben%2Bel%2Borigen.PNG\" alt=\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\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\" class=\"aligncenter  lazyload\" width=\"342\" height=\"288\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-SMOUgyC1lM4\/YJGg_MIkJTI\/AAAAAAAAFDw\/6JzXOcfZi70lpvTZtbC6y26AvTQzcnWNgCLcBGAsYHQ\/s0\/hiperbola%2Bcentrada%2Ben%2Bel%2Borigen.PNG\" alt=\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\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\" class=\"aligncenter  lazyload\" width=\"342\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span>\n<p>   &nbsp;<\/p>\n<p style=\"text-align: justify;\">\u0418 \u043e\u0442\u0441\u044e\u0434\u0430 \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span><\/td>\n<td>; \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x^2 + 2xc + c^2 + y^2} - \\sqrt{x^2 - 2xc + c^2 + y^2} = 2a<\/span><\/td>\n<td>; \u0440\u0430\u0441\u043a\u0440\u044b\u0442\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x^2 + 2xc + c^2 + y^2} = 2a + \\sqrt{x^2 - 2xc + c^2 + y^2}<\/span><\/td>\n<td>; \u043f\u0435\u0440\u0435\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\color{red}{x^2} + 2xc + \\color{purple}{c^2} + \\color{violet}{y^2} = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} + \\color{red}{x^2} - 2xc + \\color{purple}{c^2} + \\color{violet}{y^2}<\/span><\/td>\n<td>; \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043e\u0431\u0435\u0438\u0445 \u0441\u0442\u043e\u0440\u043e\u043d \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 2xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} - 2xc <\/span><\/td>\n<td>; \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 4xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u043f\u0435\u0440\u0435\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> xc = a^2 + a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> xc - a^2 = a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 -2xca^2 + a^4 = a^2(x^2 - 2xc + c^2 + y^2) <\/span><\/td>\n<td>; \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043e\u0431\u0435\u0438\u0445 \u0441\u0442\u043e\u0440\u043e\u043d \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 \\color{red}{-2xca^2} + a^4 = a^2x^2 \\color{red}{- 2xca^2} + a^2c^2 + a^2y^2 <\/span><\/td>\n<td>; \u0440\u0430\u0441\u043a\u0440\u044b\u0442\u0438\u0435 \u0441\u043a\u043e\u0431\u043e\u043a<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 + a^4 = a^2x^2 + a^2c^2 + a^2y^2 <\/span><\/td>\n<td>; \u0443\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2(c^2 - a^2) - a^2y^2 = a^2c^2 - a^4 = a^2(c^2 - a^2) <\/span><\/td>\n<td>; \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0438\u0432\u0430\u043d\u0438\u0435 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{x^2}{a^2} - \\frac{y^2}{c^2 - a^2} = 1 <\/span><\/td>\n<td>; \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0438\u0432\u0430\u043d\u0438\u0435 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<tr><\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043a\u0430\u043a \u0438 \u0434\u043b\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u043e\u0432, \u043c\u044b \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u043c <span class=\"katex-eq\" data-katex-display=\"false\">b^2=c^2-a^2<\/span> \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{ \\left(\\frac{x}{a}\\right)^2 - \\left(\\frac{y}{b}\\right)^2 = 1 }<\/span>\n<p><a name=\"3\"><\/a>     <\/p>\n<h2>\u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=801s\" target=\"_blank\" rel=\"noopener\"><strong>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong><\/a> \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043a \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-h<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-k<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0418 \u0441 \u044d\u0442\u0438\u043c \u043c\u044b \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b \u0441 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0432 \u0442\u043e\u0447\u043a\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{ \\left(\\frac{x-h}{a}\\right)^2 - \\left(\\frac{y-k}{b}\\right)^2 = 1 }<\/span>\n<p><a name=\"4\"><\/a>     <\/p>\n<h2>\u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=974s\" target=\"_blank\" rel=\"noopener\"><strong>\u0422\u0435\u043f\u0435\u0440\u044c, \u0435\u0441\u043b\u0438 \u043c\u044b \u0432\u043e\u0437\u044c\u043c\u0451\u043c \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong><\/a> \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b \u0438 \u0440\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0435\u0433\u043e, \u043c\u044b \u043f\u0440\u0438\u0434\u0451\u043c \u043a \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{x-h}{a}\\right)^2 - \\left(\\frac{y-k}{b}\\right)^2 = 1<\/span><\/td>\n<td>; \u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 (x^2 - 2xh + h^2) - a^2(y^2-2ky + y^2) = a^2b^2<\/span><\/td>\n<td>; \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0438 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0432\u0441\u0435\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">a^2b^2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2 - 2hb^2x + h^2b^2 - a^2 y^2+ 2k a^2 y - a^2 k^2 = a^2b^2<\/span><\/td>\n<td>; \u0440\u0430\u0441\u043a\u0440\u044b\u0442\u0438\u0435 \u0441\u043a\u043e\u0431\u043e\u043a<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2 - (2hb^2) x - a^2 y^2+ (2k a^2) y - (a^2b^2 + a^2 k^2 - h^2b^2) = 0 <\/span><\/td>\n<td>; \u0443\u043f\u043e\u0440\u044f\u0434\u043e\u0447\u0438\u0432\u0430\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u042d\u0442\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 <span class=\"katex-eq\" data-katex-display=\"false\">Ax^2+Bx + Cy^2 + Dy + E = 0,<\/span>, \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u0432\u0441\u0435\u0433\u0434\u0430 \u043e\u0442\u043b\u0438\u0447\u043d\u044b \u043e\u0442 \u043d\u0443\u043b\u044f \u0438 \u0438\u043c\u0435\u044e\u0442 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0435 \u0437\u043d\u0430\u043a\u0438, \u043a\u0430\u043a \u043c\u044b \u043f\u0440\u0435\u0434\u0441\u043a\u0430\u0437\u0430\u043b\u0438, \u0438\u0437\u0443\u0447\u0430\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u044b.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0432\u044b\u0432\u043e\u0434 \u0420\u0435\u0437\u044e\u043c\u0435: \u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0441\u0440\u0430\u0432\u043d\u0438\u043c \u0435\u0451 \u0441 \u044d\u043b\u043b\u0438\u043f\u0441\u043e\u043c \u0438 \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u043e\u0431\u0449\u0435\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f: \u041a \u043a\u043e\u043d\u0446\u0443 \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u0441\u043c\u043e\u0433\u0443\u0442: \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430. \u0412\u044b\u0432\u0435\u0441\u0442\u0438 \u043e\u0431\u0449\u0435\u0435 \u0438 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0438\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u0435\u0451 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u0412\u044b\u044f\u0432\u0438\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u044d\u043b\u043b\u0438\u043f\u0441\u0430\u043c\u0438 \u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430\u043c\u0438 \u0441 \u0442\u043e\u0447\u043a\u0438 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28988,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":11,"footnotes":""},"categories":[589,573],"tags":[],"class_list":["post-28997","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-589","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0432\u044b\u0432\u043e\u0434 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u0432\u0441\u0451 \u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0430\u0445: \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 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