{"id":2022,"date":"2021-12-11T09:59:18","date_gmt":"2021-12-11T00:59:18","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2022"},"modified":"2021-12-11T09:59:18","modified_gmt":"2021-12-11T00:59:18","slug":"tbr202101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr202101\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2021\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066 \\(2\\) \u3064\u306e\u5186\r\n\\[\\begin{align}\r\nC _ 1 \\ & : \\ x^2 -2x +y^2 +4y -11 = 0 \\ , \\\\\r\nC _ 2 \\ & : \\ x^2 -8x +y^2 -4y +k = 0\r\n\\end{align}\\]\r\n\u304c\u5916\u63a5\u3059\u308b\u3068\u3057, \u305d\u306e\u63a5\u70b9\u3092 P \u3068\u3059\u308b.\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(k\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000P \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5186 \\(C_1\\) \u3068\u5186 \\(C_2\\) \u306e\u5171\u901a\u63a5\u7dda\u306e\u3046\u3061\u70b9 P \u3092\u901a\u3089\u306a\u3044\u3082\u306e\u306f \\(2\\) \u672c\u3042\u308b.\r\n\u3053\u308c\u3089 \\(2\\) \u76f4\u7dda\u306e\u4ea4\u70b9 Q \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(C_1\\) \u306e\u5f0f\u3088\u308a\r\n\\[\r\n(x-1)^2 +(y+2)^2 = 16\r\n\\]\r\n\u306a\u306e\u3067, \\(C_1\\) \u306f\u4e2d\u5fc3\u304c\u70b9 A \\(( 1 , -2 )\\) , \u534a\u5f84 \\(4\\) .
    \r\n\\(C_2\\) \u306e\u5f0f\u3088\u308a\r\n\\[\r\n(x-4)^2 +(y-2)^2 = 20-k\r\n\\]\r\n\u306a\u306e\u3067, \\(C_2\\) \u306f\u4e2d\u5fc3\u304c\u70b9 B \\(( 4 , 2 )\\) , \u534a\u5f84 \\(\\sqrt{20 -k}\\) .
    \r\n\\[\r\n\\overrightarrow{\\text{AB}} = \\left( \\begin{array}{c} 3 \\\\ 4 \\end{array} \\right) \\ , \\ \\text{AB} = \\sqrt{3^2 +4^2} = 5\r\n\\]\r\n\u3086\u3048\u306b, \\(C_1 , C_2\\) \u304c\u5916\u63a5\u3059\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n4 +\\sqrt{20 -k} & = 5 \\\\\r\n\\text{\u2234} \\quad k & = \\underline{19}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\[\r\n\\overrightarrow{\\text{AP}} = \\dfrac{4}{5} \\overrightarrow{\\text{AB}} = \\left( \\begin{array}{c} \\dfrac{12}{5} \\\\ \\dfrac{16}{5} \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n\\text{P} \\ \\underline{\\left( \\dfrac{17}{5} , \\dfrac{6}{5} \\right)}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    A, B \u304b\u3089\u4e00\u65b9\u306e\u63a5\u7dda\u306b\u4e0b\u3057\u305f\u5782\u7dda\u306e\u8db3\u3092\u305d\u308c\u305e\u308c C, D \u3068\u304a\u304f\u3068,
    \r\n\\(\\triangle \\text{ACQ} \\sim \\triangle \\text{BDQ}\\) \u3067\u3042\u308a, \u76f8\u4f3c\u6bd4\u306f \\(\\text{AC} : \\text{BD} = 4 : 1\\) .
    \r\n\u3086\u3048\u306b\r\n\\[\r\n\\overrightarrow{\\text{BQ}} = \\dfrac{1}{3} \\overrightarrow{\\text{AB}} = \\left( \\begin{array}{c} 1 \\\\ \\dfrac{4}{3} \\end{array} \\right)\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{Q} \\ \\underline{\\left( 5 , \\dfrac{10}{3} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066 \\(2\\) \u3064\u306e\u5186 \\[\\begin{align} C _ 1 \\ & : \\ x^2 -2x +y^2 +4y -11 = 0 \\ , \\\\ C _ 2 \\ & : \\ x^2 -8x +y … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[178],"tags":[144,165],"class_list":["post-2022","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2021","tag-tsukuba_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=2022"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2022\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}