{"id":386,"date":"2012-05-03T00:40:27","date_gmt":"2012-05-02T15:40:27","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=386"},"modified":"2021-09-09T09:33:03","modified_gmt":"2021-09-09T00:33:03","slug":"osr201201","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201201\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2012\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(a \\gt 0\\) \u3068\u3059\u308b. \\(C _ 1\\) \u3092\u66f2\u7dda \\(x^2+\\dfrac{y^2}{a^2} =1\\) , \\(C _ 2\\) \u3092\u76f4\u7dda \\(y=2ax-3a\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u70b9 P \u304c \\(C _ 1\\) \u4e0a\u3092\u52d5\u304d, \u70b9 Q \u304c \\(C _ 2\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u7dda\u5206 PQ \u306e\u9577\u3055\u306e\u6700\u5c0f\u5024\u3092 \\(f(a)\\) \u3068\u3059\u308b. \\(f(a)\\) \u3092 \\(a\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6975\u9650\u5024 \\(\\displaystyle\\lim _ {a \\rightarrow \\infty} f(a)\\) \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

    P \\(( \\cos \\theta , a \\sin \\theta )\\) \u3068\u304a\u3051\u308b.
    \r\nP \u3092\u56fa\u5b9a\u3057\u305f\u3068\u304d, PQ \u306e\u6700\u5c0f\u5024\u306f P \u3068\u76f4\u7dda \\(C _ 2\\) \u306e\u8ddd\u96e2\u3067\u3042\u308b.
    \r\n\\(C _ 2 : \\ 2ax -y -3a =0\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{PQ} & \\geqq \\dfrac{\\left| 2a \\cos \\theta -a \\sin \\theta -3a \\right|}{\\sqrt{(2a)^2 +(-1)^2}} \\\\\r\n& = \\dfrac{\\left| \\sqrt{5} a \\cos ( \\theta +\\alpha ) -3 a \\right|}{\\sqrt{4a^2 +1}} \\\\\r\n& \\quad \\left( \\text{\u305f\u3060\u3057, } \\ \\cos \\alpha =\\dfrac{2}{\\sqrt{5}} , \\ \\sin \\alpha =\\dfrac{1}{\\sqrt{5}} \\right)\n\\end{align}\\]\r\n\u3053\u3053\u3067 P \u3092\u52d5\u304b\u3059, \u3059\u306a\u308f\u3061 \\(\\theta\\) \u3092\u52d5\u304b\u3059\u3068, \\(\\cos ( \\theta +\\alpha ) =1\\) \u306e\u3068\u304d\u306b\u6700\u5c0f\u5024\u3092\u3068\u308a\r\n\\[\r\n\\text{PQ} \\geqq \\dfrac{\\left( 3 -\\sqrt{5} \\right) a}{\\sqrt{4a^2 +1}}\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nf(a) = \\underline{\\dfrac{\\left( 3 -\\sqrt{5} \\right) a}{\\sqrt{4a^2 +1}}}\n\\]\r\n

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

    \\[\\begin{align}\r\nf(a) & = \\dfrac{3 -\\sqrt{5}}{\\sqrt{4 -\\frac{1}{a^2}}} \\\\\r\n& \\rightarrow \\dfrac{3 -\\sqrt{5}}{2} \\quad ( a \\rightarrow \\infty \\text{\u306e\u3068\u304d} )\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\displaystyle\\lim _ {a \\rightarrow \\infty} f(a) = \\underline{\\dfrac{3 -\\sqrt{5}}{2}}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a \\gt 0\\) \u3068\u3059\u308b. \\(C _ 1\\) \u3092\u66f2\u7dda \\(x^2+\\dfrac{y^2}{a^2} =1\\) , \\(C _ 2\\) \u3092\u76f4\u7dda \\(y=2ax-3a\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. … \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":[60],"tags":[142,68],"class_list":["post-386","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2012","tag-osaka_r","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/386","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=386"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/386\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=386"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}