{"id":691,"date":"2013-03-20T09:34:18","date_gmt":"2013-03-20T00:34:18","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=691"},"modified":"2021-10-30T15:40:33","modified_gmt":"2021-10-30T06:40:33","slug":"wsr200702","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr200702\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52007\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u5b9a\u6570 \\(c\\) \u306b\u5bfe\u3057\u3066\u884c\u5217 \\(A\\) \u3092\r\n\\[\r\nA = \\left( \\begin{array}{cc} 1 & c \\\\ 4 & -1 \\end{array} \\right)\r\n\\]\r\n\u3067\u5b9a\u3081, \u76f4\u7dda \\(y = x+1\\) \u4e0a\u306e\u52d5\u70b9 P \\(( t-1 , t )\\) \u3092 \\(A\\) \u306b\u3088\u3063\u3066\u79fb\u52d5\u3057\u305f\u70b9\u3092 Q \u3068\u3059\u308b. \u3059\u306a\u308f\u3061,\r\n\\[\r\nA \\left( \\begin{array}{c} t-1 \\\\ t \\end{array} \\right)\r\n\\]\r\n\u306b\u5bfe\u5fdc\u3059\u308b\u70b9\u3092 Q \u3068\u3059\u308b.\r\n\u5b9a\u70b9 R \u3068\u3059\u3079\u3066\u306e \\(t\\) \u306e\u5024\u306b\u5bfe\u3057\u3066, \u25b3PQR \u306f P \u3092\u76f4\u89d2\u306e\u9802\u70b9\u3068\u3059\u308b\u76f4\u89d2\u4e09\u89d2\u5f62\u306b\u306a\u308b\u3068\u3044\u3046. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5b9a\u70b9 R \u306e\u5ea7\u6a19\u304a\u3088\u3073\u5b9a\u6570 \\(c\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u4e09\u89d2\u5f62 PQR \u306e\u5916\u63a5\u5186\u306e\u9762\u7a4d\u306e\u6700\u5c0f\u5024\u3068, \u305d\u306e\u3068\u304d\u306e \\(t\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\[\r\n\\left( \\begin{array}{cc} 1 & c \\\\ 4 & -1 \\end{array} \\right) \\left( \\begin{array}{c} t-1 \\\\ t \\end{array} \\right) = \\left( \\begin{array}{c} (c+1)t-1 \\\\ 3t-4 \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n\\text{Q} \\ \\left( (c+1)t-1 , 3t-4 \\right)\r\n\\]\r\nR \\((u,v)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{PQ}} & = \\left( \\begin{array}{c} ct \\\\ 2t-4 \\end{array} \\right) \\\\\r\n\\overrightarrow{\\text{PR}} & = \\left( \\begin{array}{c} u-t+1 \\\\ v-t \\end{array} \\right)\r\n\\end{align}\\]\r\n\\(\\angle \\text{QPR} = 90^{\\circ}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{PQ}} \\cdot \\overrightarrow{\\text{PR}} = ct (u-t+1) +(2t-4)(v-t) & = 0 \\\\\r\n-ct^2 +c(u+1)t -2t^2 +2(v+2)t -4v & = 0 \\\\\r\n\\text{\u2234} \\quad (c+2)t^2 -\\{ c(u+1) +2(v+2) \\}t +4v & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u3059\u3079\u3066\u306e \\(t\\) \u306b\u3064\u3044\u3066\u6210\u7acb\u3059\u308b\u306e\u3067, \u4fc2\u6570\u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\\begin{gather}\r\nc+2 = 0 , \\ 4v = 0 , \\ c(u+1) +2(v+2) = 0 \\\\\r\n\\text{\u2234} \\quad c = \\underline{-2} , \\ u = 1 , \\ v = 0\r\n\\end{gather}\\]\r\n\u3088\u3063\u3066, R \\(\\underline{( 1 , 0 )}\\) .<\/p>\r\n

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

    \u8fba QR \u304c\u5916\u63a5\u5186\u306e\u76f4\u5f84\u306b\u306a\u308b\u306e\u3067, QR \u306e\u9577\u3055\u304c\u6700\u5c0f\u306e\u3068\u304d, \u5916\u63a5\u5186\u306e\u9762\u7a4d\u3082\u6700\u5c0f\u306b\u306a\u308b.
    \r\nQ \\(( -t-1 , 3t-4 )\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{QR}^2 & = (-t-2)^2 +(3t-4)^2 \\\\\r\n& = t^2 +4t +4 +9t^2 -24t +16 \\\\\r\n& = 10t^2 -20t +20 \\\\\r\n& = 10 (t-1)^2 +10 \\geqq 10\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u5916\u63a5\u5186\u306e\u9762\u7a4d\u306f, \\(t = \\underline{1}\\) \u306e\u3068\u304d, \u6700\u5c0f\u5024\r\n\\[\r\n\\pi \\left( \\dfrac{\\sqrt{10}}{2} \\right)^2 = \\underline{\\dfrac{5}{2} \\pi}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9a\u6570 \\(c\\) \u306b\u5bfe\u3057\u3066\u884c\u5217 \\(A\\) \u3092 \\[ A = \\left( \\begin{array}{cc} 1 & c \\\\ 4 & -1 \\end{array} \\right) \\] \u3067\u5b9a\u3081, \u76f4\u7dda \\(y = x … \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":[99],"tags":[147,109],"class_list":["post-691","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2007","tag-waseda_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/691","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=691"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/691\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=691"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=691"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}