{"id":654,"date":"2023-07-06T17:52:02","date_gmt":"2023-07-06T14:52:02","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=654"},"modified":"2025-09-04T17:43:41","modified_gmt":"2025-09-04T14:43:41","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%bb%d0%b5%d1%82%d0%be-2023-%d0%b2%d0%b0%d1%80%d0%b8%d0%b0%d0%bd%d1%82-35582-%d0%b7%d0%b0%d0%b4%d0%b0%d0%bd%d0%b8%d0%b5-1","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=654","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u041b\u0415\u0422\u041e 2023, \u0412\u0410\u0420\u0418\u0410\u041d\u0422 35582, \u0417\u0410\u0414\u0410\u041d\u0418\u0415 1"},"content":{"rendered":"\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" data-id=\"655\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/49-1024x466.png\" alt=\"\" class=\"wp-image-655\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/49-1024x466.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/49-300x137.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/49-768x349.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/49.png 1424w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"637\" data-id=\"656\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/50-1024x637.png\" alt=\"\" class=\"wp-image-656\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/50-1024x637.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/50-300x187.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/50-768x478.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/50.png 1460w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/6\/RUS\/35582.pdf\" data-type=\"link\" data-id=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/6\/RUS\/35582.pdf\">\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spoiler-wrap\">\n\t\t\t\t<div class=\"spoiler-head folded\">\u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/div>\n\t\t\t\t<div class=\"spoiler-body\"><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">(1) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(\u05d0)<\/strong><\/mark> \u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0432 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\) \\((a&gt;b\\))<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \\(a\\) &#8212; \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0434\u043e \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u043e\u0441\u044c\u044e \\(X\\), \\(b\\)- \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0434\u043e \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0441 \u043e\u0441\u044c\u044e \\(Y\\)  (\u0441\u043c. \u0440\u0438\u0441. 1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0430\u043d\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u043b\u043b\u0438\u043f\u0441\u0430: \\(\\frac{x^2}{144}+\\frac{y^2}{144-4k^2}=1\\), \\(0&lt;k&lt;6\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0441\u044e\u0434\u0430 \\(a=\\sqrt{144}=12\\), \\(b=\\sqrt{144-4k^2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0424\u043e\u043a\u0443\u0441\u044b \u044d\u043b\u043b\u0438\u043f\u0441\u0430 &#8212; \u0442\u043e\u0447\u043a\u0438 \\(F_1\\) \u0438 \\(F_2\\). \u041e\u043d\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0443\u044e\u0442\u0441\u044f \u0442\u0435\u043c, \u0447\u0442\u043e \u0441\u0443\u043c\u043c\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u044d\u043b\u043b\u0438\u043f\u0441\u0430 \u0434\u043e \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043b\u0435\u0436\u0430\u0449\u0435\u0439 \u043d\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0435 \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438. \u0422\u043e \u0435\u0441\u0442\u044c \u0441\u0443\u043c\u043c\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043e\u0442 \\(F_1\\) \u0438 \\(F_2\\) \u0434\u043e \u0442\u043e\u0447\u043a\u0438 \\(K\\) \u0440\u0430\u0432\u043d\u043e \u0441\u0443\u043c\u043c\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043e\u0442 \\(F_1\\) \u0438 \\(F_2\\) \u0434\u043e \u0442\u043e\u0447\u043a\u0438 \\(L\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0443\u0441\u0442\u044c \\(F_2O=OF_1=m\\) (\u0441\u043c. \u0440\u0438\u0441. 2).  \\(m\\) &#8212; \u044d\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0438\u0437 \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u0434\u043e \u0446\u0435\u043d\u0442\u0440\u0430 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u044d\u043b\u043b\u0438\u043f\u0441\u0430. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(m\\) \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(m=\\sqrt{a^2-b^2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(m=\\sqrt{144-(144-4k^2}=2k\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \\(F_2K+F_1K=2m+12-m+12-m=24\\) (*)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( F_2L=LF_1\\), \u0442\u0430\u043a \u043a\u0430\u043a \\(\\Delta F_2LO=\\Delta F_2LO\\) \u043f\u043e \u0434\u0432\u0443\u043c \u043a\u0430\u0442\u0435\u0442\u0430\u043c. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \u0422\u043e\u0433\u0434\u0430: \\( F_2L+LF_1=2\\sqrt{m^2+(\\sqrt{144-4k^2})^2}=24\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( \\sqrt{m^2+({144-4k^2})}=12\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(m^2+{144-4k^2}=144\\), \\(m^2=4k^2\\), \\(m=2k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0444\u043e\u043a\u0443\u0441\u043e\u0432 \u044d\u043b\u043b\u0438\u043f\u0441\u0430:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(F_1(2k,0)\\), \\(F_2(-2k,0)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442: <\/em>\\(F_1(2k,0)\\), \\(F_2(-2k,0)\\)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1006\" height=\"704\" data-id=\"686\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/55-1.png\" alt=\"\" class=\"wp-image-686\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/55-1.png 1006w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/55-1-300x210.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/55-1-768x537.png 768w\" sizes=\"auto, (max-width: 1006px) 100vw, 1006px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 1<\/figcaption><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"718\" data-id=\"688\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/56-1024x718.png\" alt=\"\" class=\"wp-image-688\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/56-1024x718.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/56-300x210.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/56-768x539.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/56.png 1038w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441.2<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(\u05d1)<\/strong><\/mark> (1) \u0412\u043e\u0437\u044c\u043c\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \\(A\\) \u0432  \u043f\u0435\u0440\u0432\u043e\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u043d\u0442\u0435. \u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0437\u0430\u0434\u0430\u0447\u0438 \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u043b\u0435\u0436\u0438\u0442 \u043d\u0430 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0435, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u043c, \u0430 \u0444\u043e\u043a\u0443\u0441 \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d \u0432 \u0442\u043e\u0447\u043a\u0435  \\(F_1\\), \u0442\u0430\u043a, \u0447\u0442\u043e \\(AF_1=10k\\). \u0412\u044b\u0440\u0430\u0437\u0438\u043c \u0447\u0435\u0440\u0435\u0437 \\(k\\) \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u043e\u0439 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043c\u0435\u0441\u0442\u043e \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0435\u043d\u043d\u044b\u0445 \u043e\u0442 \u0434\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 F, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0439&nbsp;<strong>\u0444\u043e\u043a\u0443\u0441\u043e\u043c&nbsp;<\/strong>\u0438 \u0434\u0430\u043d\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0439&nbsp;<strong>\u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u043e\u0439.<\/strong> \u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 \\(y^2=2px\\). \u041f\u0440\u0438\u0447\u0435\u043c \u0444\u043e\u043a\u0443\u0441 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \\((\\frac{p}{2},0)\\),  \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b \\(x=-\\frac{p}{2}\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0437\u0430\u0434\u0430\u0447\u0438 \u0444\u043e\u043a\u0443\u0441 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d \u0432 \u0442\u043e\u0447\u043a\u0435  \\(F_1\\), \u0430 \u0437\u043d\u0430\u0447\u0438\u0442 \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \\(F_1(2k,0)\\). \u0417\u043d\u0430\u0447\u0438\u0442, \\(\\frac{p}{2}=2k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b \\(x=-\\frac{p}{2}=-2k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em>  \\(x=-2k\\)<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">(2) \u0412\u044b\u0440\u0430\u0437\u0438\u043c \u0447\u0435\u0440\u0435\u0437 \\(k\\) \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(A\\), \u0435\u0441\u043b\u0438 \\(AF_1=10k\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u043f\u0443\u0441\u0442\u0438\u043c \u0438\u0437 \u0442\u043e\u0447\u043a\u0438 \\(A\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440 \\(AD\\)  \u043d\u0430 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440 \\(AB\\) \u043d\u0430 \u043e\u0441\u044c \\(X\\). \u0422\u043e\u0433\u0434\u0430 \u0434\u043b\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\(AD\\) \u0440\u0430\u0432\u043d\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \\(A\\) \u0434\u043e \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0447\u043a\u0430 \\(C\\) &#8212; \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b \u0441 \u043e\u0441\u044c\u044e  \\(X\\). <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-5 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"556\" data-id=\"669\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/53-1024x556.png\" alt=\"\" class=\"wp-image-669\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/53-1024x556.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/53-300x163.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/53-768x417.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/53.png 1120w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 3<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u043b\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\(AF_1\\) \u0440\u0430\u0432\u043d\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \\(A\\) \u0434\u043e \u0444\u043e\u043a\u0443\u0441\u0430 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \\(AF_1=AD=10k\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u043e\u0442 \u0442\u043e\u0447\u0435\u043a \\(C\\) \u0438 \\(F_1\\) \u0434\u043e \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0430 \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442, \u0440\u0430\u0432\u043d\u044b \u043f\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438 \u0440\u0430\u0432\u043d\u044b \\(2k\\). \u0422\u043e\u0433\u0434\u0430 \u0434\u043b\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430  \\(CF_1\\) \u0440\u0430\u0432\u043d\u0430 \\(4k\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(AD=BC=10k\\), \u0442\u043e\u0433\u0434\u0430 \\(F_1B=BC-CF_1=10k-4k=6k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \\(\\Delta F_1AB\\). \u041f\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430 \\(AB=8k\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438  \\(B\\) \u0434\u043e \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0440\u0430\u0432\u043d\u043e \\(2k+6k=8k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0441\u044e\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(A(8k,8k)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442: <\/em>\\(A(8k,8k)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(\u05d2)<\/strong><\/mark> \u041d\u0430\u0439\u0434\u0435\u043c \\(k\\), \u0435\u0441\u043b\u0438 \\(AF_1\\) &#8212; \u0434\u0438\u0430\u043c\u0435\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u044f\u043c\u0430\u044f, \u0437\u0430\u0434\u0430\u043d\u043d\u0430\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \\(5x+12y=138\\) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043a \u044d\u0442\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438  \\(AF_1\\) &#8212; \u0434\u0438\u0430\u043c\u0435\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0440\u0430\u0434\u0438\u0443\u0441 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u0435\u043d \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435 \u0434\u043b\u0438\u043d\u044b \u0434\u0438\u0430\u043c\u0435\u0442\u0440\u0430, \u0430 \u0446\u0435\u043d\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u043b\u0435\u0436\u0438\u0442 \u0432 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u0435 \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\(AF_1\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438  \\(F_1(2k,0)\\),  \u0442\u043e\u0447\u043a\u0438 \\(A(8k,8k)\\), \u0442\u043e\u0433\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\((\\frac{2k+8k}{2}, \\frac{0+8k}{2})\\), \u0442\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0446\u0435\u043d\u0442\u0440\u0430 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \\((5k,4k)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \\(AF_1=2R=10k\\), \u043e\u0442\u0441\u044e\u0434\u0430 \\(R=5k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 \\((x-x_0)^2+(y-y_0)^2=R^2\\), \u0433\u0434\u0435 \\((x_0,y_0)\\) &#8212; \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0446\u0435\u043d\u0442\u0440\u0430 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0430\u0448\u0435\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\((x-5k)^2+(y-4k)^2=25k^2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0442\u043e\u0447\u043a\u0430 \\(Q(5k,4k)\\) &#8212; \u0446\u0435\u043d\u0442\u0440 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 \u043f\u0440\u044f\u043c\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043a \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0446\u0435\u043d\u0442\u0440\u0430 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 \u0434\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u0440\u0430\u0432\u043d\u043e \u0440\u0430\u0434\u0438\u0443\u0441\u0443 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438. <a rel=\"noreferrer noopener\" href=\"https:\/\/ege-ok.ru\/2016\/05\/04\/rasstoyanie-ot-tochki-do-pryamoj-na-ploskosti-metod-koordinat\" target=\"_blank\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438<\/a> \\(Q(x_0, y_0)\\)  <a href=\"https:\/\/ege-ok.ru\/2016\/05\/04\/rasstoyanie-ot-tochki-do-pryamoj-na-ploskosti-metod-koordinat\" target=\"_blank\" rel=\"noreferrer noopener\">\u0434\u043e \u043f\u0440\u044f\u043c\u043e\u0439<\/a>  \\(ax+by+c=0\\) \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u044b: <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\rho=\\frac{|ax_0+by_0+c|}{\\sqrt{a^2+b^2}}\\) (**)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \\(Q(5k,4k)\\) \u0434\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \\(5x+12y-138=0\\) \u0440\u0430\u0432\u043d\u043e \\(5k\\). \u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u044d\u0442\u0438 \u0434\u0430\u043d\u043d\u044b\u0435 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 (**):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(5k=\\frac{|5\\cdot 5k+12\\cdot 4k-138|}{\\sqrt{5^2+12^2}}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(5k=\\frac{|73k-138|}{13}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(65k=|73k-138|\\), \u043e\u0442\u0441\u044e\u0434\u0430:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(73k-138=65k\\) \u0438\u043b\u0438 \\(73k-138=-65k\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(8k=138\\) \u0438\u043b\u0438 \\(138k=138\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(k=17.25\\) \u0438\u043b\u0438 \\(k=1\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439 \u043d\u0430 \\(k\\)  (\\(1\\le k \\le 6\\)) (\u043f\u043e\u0445\u043e\u0436\u0435, \u0432 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0437\u0430\u043a\u0440\u0430\u043b\u0430\u0441\u044c \u043e\u043f\u0435\u0447\u0430\u0442\u043a\u0430), \\(k=1\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442: <\/em>  \\(k=1\\)<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>(\u05d3)<\/strong><\/mark> \u0421\u0440\u0430\u0432\u043d\u0438\u043c \u043f\u0435\u0440\u0438\u043c\u0435\u0442\u0440\u044b \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \\(F_1AF_2\\) \u0438 \\(F_1DF_2\\), \u0433\u0434\u0435 \\(D\\) &#8212; \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u044d\u043b\u043b\u0438\u043f\u0441\u0435. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(P_{\\Delta F_1DF_2}=F_2D+F_1D+F_2F_1=F_2K+F_1K+F_2F_1\\) \u043f\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u044d\u043b\u043b\u0438\u043f\u0441\u0430. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0437 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 (*) \\(F_2K+F_1K=24\\), \\(F_2F_1=4k=4\\), \u0442\u043e\u0433\u0434\u0430 \\(P_{\\Delta F_1DF_2}=28\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(P_{\\Delta F_1AF_2}=F_2A+F_1A+F_2F_1\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(F_1A=10k=10\\), \\(F_2A=\\sqrt{F_2^2+AB^2}=\\sqrt{10^2+8^2}=\\sqrt{164}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \\(P_{\\Delta F_1AF_2}=10+\\sqrt{164}+4\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a \u043a\u0430\u043a \\(\\sqrt{164}&lt;13\\), \\(P_{\\Delta F_1AF_2}=&lt;27\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(P_{\\Delta F_1AF_2} &lt;P_{\\Delta F_1AF_2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442: <\/em>\\(P_{\\Delta F_1AF_2} &lt;P_{\\Delta F_1AF_2}\\)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-6 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"808\" height=\"492\" data-id=\"698\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/57.png\" alt=\"\" class=\"wp-image-698\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/57.png 808w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/57-300x183.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/57-768x468.png 768w\" sizes=\"auto, (max-width: 808px) 100vw, 808px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441. 4<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div>\n\t\t\t<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-654","post","type-post","status-publish","format-standard","hentry","category-12"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=654"}],"version-history":[{"count":45,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/654\/revisions"}],"predecessor-version":[{"id":1313,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/654\/revisions\/1313"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}