{"id":149,"date":"2011-12-01T17:41:55","date_gmt":"2011-12-01T08:41:55","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=149"},"modified":"2021-10-29T08:35:15","modified_gmt":"2021-10-28T23:35:15","slug":"wsr201001","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201001\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52010\uff1a\u7b2c1\u554f"},"content":{"rendered":"
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\\(xy\\) \u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\((-1, 4)\\) , B \\((2, 5)\\) \u3092\u901a\u308a, \u76f4\u7dda \\(y = \\dfrac{1}{2}x\\) \u3068\u5171\u6709\u70b9\u3092\u3082\u3064\u5186\u3092\u8003\u3048\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u3053\u306e\u5186\u306e\u4e2d\u5fc3 P \u306e\u8ecc\u8de1\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u3053\u306e\u5186\u306e\u534a\u5f84 \\(r\\) \u306e\u6700\u5c0f\u5024\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

    \u4e2d\u5fc3 P \u306f, \u7dda\u5206 AB \u306e\u5782\u76f4\u4e8c\u7b49\u5206\u7dda \\(m\\) \u4e0a\u306b\u3042\u308b.\r\n\\[\\begin{align}\r\n\\text{AB \u306e\u50be\u304d} & : \\ \\dfrac{5-4}{2-(-1)} = \\dfrac{1}{3} , \\\\\r\n\\text{AB \u306e\u4e2d\u70b9} & : \\ \\left( \\dfrac{-1+2}{2} , \\dfrac{4+5}{2} \\right) = \\left( \\dfrac{1}{2} , \\dfrac{9}{2} \\right)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\r\nm : \\ y = -3 \\left( x -\\dfrac{1}{2} \\right) +\\dfrac{9}{2} = -3x +6\r\n\\]\r\nP \\(\\left( p , -3p+6 \\right)\\) \u3068\u304a\u304f\u3068, \u5186\u306e\u534a\u5f84 \\(r\\) \u306f\r\n\\[\\begin{align}\r\nr^2 & = ( p-2 )^2 + ( -3p+6 -5 )^2 \\\\\r\n& = 10p^2 -10p +5 \\quad ... [1]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u5186\u306e\u65b9\u7a0b\u5f0f\u306f\r\n\\[\r\n\\left( x-p \\right)^2 +\\left( y +3p -6 \\right)^2 = 10p^2 -10p +5\r\n\\]\r\n\u3053\u308c\u306b \\(y = \\dfrac{1}{2}\\) \u3059\u306a\u308f\u3061 \\(x = 2y\\) \u3092\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n\\left( 2y-p \\right)^2 +\\left( y +3p -6 \\right)^2 & = 10p^2 -10p +5 \\\\\r\n4y^2 -4py +p^2 +y^2 +6( p-2 )y +9( p-2 )^2 & = 10p^2 -10p +5 \\\\\r\n\\text{\u2234} \\quad 5y^2 +2( p-6 )y -26p +31 & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u5b9f\u6570\u89e3 \\(y\\) \u3092\u3082\u3064\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u306e\u3067, \u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} & = ( p-6 )^2 -5( -26p +31 ) \\\\\r\n& = p^2 +118p -119 \\\\\r\n& = ( p-1 )( p+119 ) \\geqq 0 \\\\\r\n\\text{\u2234} \\quad p & \\leqq -119 , 1 \\leqq p \\quad ... [2]\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u8ecc\u8de1\u306f\r\n\\[\r\n\\underline{\\text{\u534a\u76f4\u7dda} : \\ y = -3x +6 \\ \\left( x \\leqq -119 , 1 \\leqq x \\right)}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\nr^2 & = 10p^2 -10p +5 \\\\\r\n& = 10 \\left( p-\\dfrac{1}{2} \\right)^2 +\\dfrac{2}{5}\r\n\\end{align}\\]\r\n\u3053\u308c\u306e [2] \u306b\u304a\u3051\u308b\u6700\u5c0f\u5024\u306f \\(p=1\\) \u306e\u3068\u304d\u3067\r\n\\[\r\n10 \\cdot 1^2 - 10 \\cdot 1 +5 = 5\r\n\\]\r\n\u3088\u3063\u3066, \\(r\\) \u306e\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{\\sqrt{5}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\((-1, 4)\\) , B \\((2, 5)\\) \u3092\u901a\u308a, \u76f4\u7dda \\(y = \\dfrac{1}{2}x\\) \u3068\u5171\u6709\u70b9\u3092\u3082\u3064\u5186\u3092\u8003\u3048\u308b. \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u3053\u306e … \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":[37],"tags":[147,14],"class_list":["post-149","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2010","tag-waseda_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/149","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=149"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/149\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}