{"id":98,"date":"2011-11-27T18:48:19","date_gmt":"2011-11-27T09:48:19","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=98"},"modified":"2021-03-18T09:58:51","modified_gmt":"2021-03-18T00:58:51","slug":"tkr201004","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201004\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2010\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u66f2\u7dda\r\n\\[\r\nC : \\ y = \\dfrac{1}{2} x + \\sqrt{\\dfrac{1}{4} x^2 + 2}\r\n\\]\r\n\u3068 , \u305d\u306e\u4e0a\u306e\u76f8\u7570\u306a\u308b \\(2\\) \u70b9 \\(\\text{P} {} _ 1 ( x _ 1 , y _ 1 )\\) , \\(\\text{P} {} _ 2 ( x _ 2 , y _ 2 )\\) \u3092\u8003\u3048\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\text{P} {} _ i\\) \uff08 \\(i = 1 , 2\\) \uff09\u3092\u901a\u308b \\(x\\) \u8ef8\u306b\u5e73\u884c\u306a\u76f4\u7dda\u3068, \u76f4\u7dda \\(y = x\\) \u3068\u306e\u4ea4\u70b9\u3092, \u305d\u308c\u305e\u308c \\(\\text{H} {} _ i\\) \uff08 \\(i = 1 , 2\\) \uff09\u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \\(\\triangle \\text{OP} {} _ 1 \\text{H} {} _ 1\\) \u3068 \\(\\triangle \\text{OP} {} _ 2 \\text{H} {} _ 2\\) \u306e\u9762\u7a4d\u306f\u7b49\u3057\u3044\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(x _ 1 \\lt x _ 2\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d \\(C\\) \u306e \\(x _ 1 \\leqq x \\leqq x _ 2\\) \u306e\u7bc4\u56f2\u306b\u3042\u308b\u90e8\u5206\u3068, \u7dda\u5206 \\(\\text{P} {} _ 1 \\text{O}\\) , \\(\\text{P} {} _ 2 \\text{O}\\) \u3068\u3067\u56f2\u307e\u308c\u308b\u56f3\u5f62\u306e\u9762\u7a4d\u3092, \\(y _ 1 , y _ 2\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(C\\) \u306e\u5f0f\u3088\u308a\r\n\\[\r\ny -\\dfrac{1}{2} x \\geqq 0 \\quad ... [1]\r\n\\]\r\n\u3053\u306e\u3082\u3068\u3067, \\(C\\) \u306e\u5f0f\u3092 \\(x\\) \u306b\u3064\u3044\u3066\u3068\u304f\u3068\r\n\\[\\begin{align}\r\n\\left( y -\\dfrac{1}{2} x \\right)^2 & = \\dfrac{1}{4} x^2 + 2 \\\\\r\ny^2 -xy & = 2 \\\\\r\n\\text{\u2234} \\quad x & = y -\\dfrac{2}{y}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1]\u306b\u3082\u6ce8\u610f\u3059\u308c\u3070 \\(C\\) \u306f\u4e0b\u56f3\u306e\u3068\u304a\u308a.<\/p>\r\n\"\"<\/p>\r\n

    \u4e00\u822c\u306b, P \\(( x , y )\\) \u306b\u5bfe\u3057\u3066, H \\(( y , y )\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\triangle \\text{OPH} & = \\dfrac{1}{2} \\left( y -x \\right) y \\\\\r\n& = \\dfrac{1}{2} \\cdot \\dfrac{2}{y} \\cdot y \\\\\r\n& = 1\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(x\\) \u306b\u3088\u3089\u305a\u4e00\u5b9a\u306a\u306e\u3067\r\n\\[\r\n\\triangle \\text{OP} {} _ 1 \\text{H} {} _ 1 = \\triangle \\text{OP} {} _ 2 \\text{H} {} _ 2\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f, \\(C\\) , \\(y=x\\) , \\(y=y _ 1\\) , \\(y=y _ 2\\) \u306b\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u306b\u7b49\u3057\u3044\u306e\u3067\r\n\\[\\begin{align}\r\nS & = \\displaystyle\\int _ {y _ 1}^{y _ 2} \\left| y - \\left( y -\\dfrac{2}{y} \\right) \\right| \\, dy \\\\\r\n& = \\displaystyle\\int _ {y _ 1}^{y _ 2} \\left| \\dfrac{2}{y} \\right| \\, dy \\\\\r\n& = 2 \\left[ \\log y \\right] _ {y _ 1}^{y _ 2} \\\\\r\n& = \\underline{ 2 \\log \\dfrac{y _ 2}{y _ 1} }\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u66f2\u7dda \\[ C : \\ y = \\dfrac{1}{2} x + \\sqrt{\\dfrac{1}{4} x^2 + 2} \\] \u3068 , \u305d\u306e\u4e0a\u306e\u76f8\u7570\u306a\u308b \\(2\\) \u70b9 \\(\\text{P} … \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":[19],"tags":[139,14],"class_list":["post-98","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2010","tag-tokyo_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/98","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=98"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/98\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=98"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=98"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=98"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}