{"id":937,"date":"2013-09-16T23:46:41","date_gmt":"2013-09-16T14:46:41","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=937"},"modified":"2021-10-23T03:19:11","modified_gmt":"2021-10-22T18:19:11","slug":"wsr201301","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201301\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52013\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u653e\u7269\u7dda \\(C : \\ y^2 = 4px \\ (p \\gt 0 )\\) \u306e\u7126\u70b9 F \\(( p , 0 )\\) \u3092\u901a\u308b \\(2\\) \u76f4\u7dda \\(\\ell _ 1 , \\ell _ 2\\) \u306f\u4e92\u3044\u306b\u76f4\u4ea4\u3057, \\(C\\) \u3068 \\(\\ell _ 1\\) \u306f \\(2\\) \u70b9 \\(\\text{P} _ 1 , \\text{P} _ 2\\) \u3067, \\(C\\) \u3068 \\(\\ell _ 2\\) \u306f \\(2\\) \u70b9 \\(\\text{Q} _ 1 , \\text{Q} _ 2\\) \u3067\u4ea4\u308f\u308b\u3068\u3059\u308b. \u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\ell _ 1\\) \u306e\u65b9\u7a0b\u5f0f\u3092 \\(x = ay+p\\) \u3068\u7f6e\u304d, \\(\\text{P} _ 1 , \\text{P} _ 2\\) \u306e\u5ea7\u6a19\u3092\u305d\u308c\u305e\u308c \\(( x _ 1 , y _ 1 ) , \\ ( x _ 2 , y _ 2 )\\) \u3068\u3059\u308b. \\(y _ 1 +y _ 2 , \\ y _ 1 y _ 2\\) \u3092 \\(a\\) \u3068 \\(p\\) \u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\dfrac{1}{\\text{P} _ 1 \\text{P} _ 2} +\\dfrac{1}{\\text{Q} _ 1 \\text{Q} _ 2}\\) \u306f \\(\\ell _ 1 , \\ell _ 2\\) \u306e\u3068\u308a\u65b9\u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(C\\) \u306e\u5f0f\u3068 \\(\\ell _ 1\\) \u306e\u5f0f\u304b\u3089 \\(x\\) \u3092\u6d88\u53bb\u3057\u3066\r\n\\[\\begin{gather}\r\ny^2 = 4p( ay+p ) \\\\\r\n\\text{\u2234} \\quad y^2 -4pay -4p^2 = 0\r\n\\end{gather}\\]\r\n\u3053\u306e\u65b9\u7a0b\u5f0f\u306e \\(2\\) \u89e3\u304c \\(y _ 1 , y _ 2\\) \u306a\u306e\u3067, \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\ny _ 1 +y _ 2 = \\underline{4pa} , \\ y _ 1 y _ 2 = \\underline{-4p^2}\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\left| y _ 1 -y _ 2 \\right| & = \\sqrt{( y _ 1 +y _ 2 )^2 -4 y _ 1 y _ 2} \\\\\r\n& = \\sqrt{(4pa)^2 -4 (-4p^2)} \\\\\r\n& = 4p \\sqrt{a^2+1}\r\n\\end{align}\\]\r\n\\(\\ell _ 1\\) \u306e\u50be\u304d\u306f \\(a\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{P} _ 1\\text{P} _ 2 & = \\sqrt{1+a^2} \\left| y _ 1 -y _ 2 \\right| \\\\\r\n& = 4p ( a^2+1 ) \\quad ... [1]\r\n\\end{align}\\]\r\n\\(\\ell _ 2\\) \u306b\u5bfe\u3057\u3066\u3082\u540c\u69d8\u306b\u8003\u3048\u308b\u3068, \\(\\ell _ 2\\) \u306e\u50be\u304d\u306f \\(-\\dfrac{1}{a}\\) \u306a\u306e\u3067, [1] \u306b\u304a\u3044\u3066 \\(a \\rightarrow -\\dfrac{1}{a}\\) \u3068\u7f6e\u304d\u63db\u3048\u308c\u3070\u3088\u304f\r\n\\[\\begin{align}\r\n\\text{Q} _ 1\\text{Q} _ 2 & = 4p \\left\\{ \\left( -\\dfrac{1}{a} \\right)^2 +1 \\right\\} \\\\\r\n& = \\dfrac{4p ( a^2+1 )}{a^2} \\quad ... [2]\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, [1] [2] \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{1}{\\text{P} _ 1\\text{P} _ 2} +\\dfrac{1}{\\text{Q} _ 1\\text{Q} _ 2} & = \\dfrac{1}{4p^2 (a^2+1)} +\\dfrac{a^2}{4p^2 (a^2+1)} \\\\\r\n& = \\dfrac{1}{4p}\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(a\\) \u306b\u3088\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u653e\u7269\u7dda \\(C : \\ y^2 = 4px \\ (p \\gt 0 )\\) \u306e\u7126\u70b9 F \\(( p , 0 )\\) \u3092\u901a\u308b \\(2\\) \u76f4\u7dda \\(\\ell _ 1 , \\ell _ 2\\) \u306f\u4e92\u3044\u306b\u76f4\u4ea4\u3057, \\(C\\) \u3068 … \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":[100],"tags":[147,111],"class_list":["post-937","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2013","tag-waseda_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/937","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=937"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/937\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=937"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=937"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}