{"id":699,"date":"2013-03-26T21:21:20","date_gmt":"2013-03-26T12:21:20","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=699"},"modified":"2021-10-04T18:11:59","modified_gmt":"2021-10-04T09:11:59","slug":"kbr200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr200701\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2007\uff1a\u7b2c1\u554f"},"content":{"rendered":"
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\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(2\\) \u5b9a\u70b9 A \\((1,0)\\) \u3068 O \\((0,0)\\) \u3092\u3068\u308b.\r\n\u307e\u305f, \\(m\\) \u3092 \\(1\\) \u3088\u308a\u5927\u304d\u3044\u5b9f\u6570\u3068\u3059\u308b.<\/p>\r\n

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  1. (1)<\/strong>\u3000\\(\\text{AP} : \\text{OP} = m : 1\\) \u3092\u6e80\u305f\u3059\u70b9 P \\((x,y)\\) \u306e\u8ecc\u8de1\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 A \u3092\u901a\u308b\u76f4\u7dda\u3067, (1)<\/strong> \u3067\u6c42\u3081\u305f\u8ecc\u8de1\u3068\u306e\u5171\u6709\u70b9\u304c \\(1\\) \u500b\u306e\u3082\u306e\u3092\u6c42\u3081\u3088. \u307e\u305f, \u305d\u306e\u5171\u6709\u70b9\u306e\u5ea7\u6a19\u3082\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n\"tsukuba_r_2007_01_01\"\r\n

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

    \\(\\text{AP}^2 = m^2 \\text{OP}^2\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n(x-1)^2 +y^2 & = m^2 \\left( x^2+y^2 \\right) \\\\\r\nx^2 +\\dfrac{2x}{m^2-1} +y^2 & = \\dfrac{1}{m^2-1} \\\\\r\n\\left( x +\\dfrac{1}{m^2-1} \\right)^2 +y^2 & = \\dfrac{1}{m^2-1} +\\dfrac{1}{(m^2-1)^2} \\\\\r\n\\text{\u2234} \\quad \\left( x +\\dfrac{1}{m^2-1} \\right)^2 +y^2 & = \\left( \\dfrac{m}{m^2-1} \\right)^2\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\u70b9 P \u306e\u8ecc\u8de1\u306f\r\n\\[\r\n\\underline{\\text{\u5186} : \\ \\left( x +\\dfrac{1}{m^2-1} \\right)^2 +y^2 = \\left( \\dfrac{m}{m^2-1} \\right)^2}\r\n\\]\r\n

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

    \u70b9 A \u3092\u901a\u308b\u76f4\u7dda\u3092 \\(\\ell : \\ y = k(x-1)\\) \u3068\u304a\u304f\u3068, \\(\\ell\\) \u306f\u70b9 P \u306e\u8ecc\u8de1\u3067\u3042\u308b\u5186\u3068\u63a5\u3059\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{\\left| -\\frac{k}{m^2-1} -0 -k \\right|}{\\sqrt{k^2+1}} & = \\dfrac{m}{m^2-1} \\\\\r\nkm & = \\sqrt{k^2+1} \\\\\r\nk^2 m^2 & = k^2+1 \\\\\r\n\\text{\u2234} \\quad k & = \\pm \\dfrac{1}{\\sqrt{m^2-1}}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u76f4\u7dda\u306e\u5f0f\u306f\r\n\\[\r\n\\underline{y = \\pm \\dfrac{x-1}{\\sqrt{m^2-1}}}\r\n\\]\r\n\u5171\u6709\u70b9\u306e\u5ea7\u6a19\u3092 \\((X,Y)\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nY = \\pm \\dfrac{X-1}{\\sqrt{m^2-1}} \\quad ... [1]\r\n\\]\r\n\u307e\u305f, \u5186\u306e\u4e2d\u5fc3\u3068\u63a5\u70b9\u3092\u7d50\u3076\u7dda\u5206\u306f\u50be\u304d\u304c \\(\\mp \\sqrt{m^2-1}\\) \u306a\u306e\u3067\r\n\\[\r\nY = \\mp \\sqrt{m^2-1} \\left( X +\\dfrac{1}{m^2-1} \\right) \\quad ... [2]\r\n\\]\r\n[1] [2] \u3088\u308a\r\n\\[\\begin{align}\r\n\\pm \\dfrac{X-1}{\\sqrt{m^2-1}} & = \\mp \\sqrt{m^2-1} \\left( X +\\dfrac{1}{m^2-1} \\right) \\\\\r\nX-1 & = -(m^2-1) X -1 \\\\\r\n\\text{\u2234} \\quad X & = 0\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\r\nY = \\mp \\dfrac{1}{\\sqrt{m^2-1}}\r\n\\]\r\n\u3088\u3063\u3066, \u5171\u6709\u70b9\u306e\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( 0 , \\mp \\dfrac{1}{\\sqrt{m^2-1}} \\right)}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(2\\) \u5b9a\u70b9 A \\((1,0)\\) \u3068 O \\((0,0)\\) \u3092\u3068\u308b. \u307e\u305f, \\(m\\) \u3092 \\(1\\) \u3088\u308a\u5927\u304d\u3044\u5b9f\u6570\u3068\u3059\u308b. (1)\u3000\\(\\text{AP} : \\text{OP} … \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":[101],"tags":[144,109],"class_list":["post-699","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2007","tag-tsukuba_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/699","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=699"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/699\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}