{"id":705,"date":"2013-03-29T23:23:20","date_gmt":"2013-03-29T14:23:20","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=705"},"modified":"2021-10-04T19:18:02","modified_gmt":"2021-10-04T10:18:02","slug":"kbr200706","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr200706\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2007\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u4e0a\u3067, \\(2\\) \u6b21\u66f2\u7dda \\(C : \\ x^2+ay^2+by = 0\\) \u304c\u76f4\u7dda \\(L : \\ y = 2x-1\\) \u306b\u70b9 P \u3067\u63a5\u3057\u3066\u3044\u308b.\r\n\u305f\u3060\u3057, \\(a \\neq -\\dfrac{1}{4}\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(a\\) \u3068 \\(b\\) \u306e\u95a2\u4fc2\u5f0f\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(C\\) \u304c\u6955\u5186, \u653e\u7269\u7dda, \u53cc\u66f2\u7dda\u3068\u306a\u308b\u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b, \\(b\\) \u306e\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(C\\) \u304c\u6955\u5186\u3068\u3059\u308b\u5834\u5408\u306e\u63a5\u70b9P\u306e\u5b58\u5728\u7bc4\u56f2\u3092\u6c42\u3081, \\(xy\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(b = 0\\) \u306e\u3068\u304d, \\(C\\) \u306f \\(2\\) \u6b21\u66f2\u7dda\u3092\u8868\u3055\u306a\u3044\u306e\u3067\r\n\\[\r\nb \\neq 0 \\quad ... [1]\r\n\\]\r\n\u4ee5\u4e0b\u3067\u306f, [1] \u306e\u3082\u3068\u3067\u8003\u3048\u308b.\r\n\\(L\\) \u306e\u5f0f\u3088\u308a\r\n\\[\r\nx = \\dfrac{y+1}{2}\r\n\\]\r\n\u3053\u308c\u3092 \\(C\\) \u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n(y+1)^2 +4ay^2 +4by & = 0 \\\\\r\n\\text{\u2234} \\quad (4a+1) y^2 +2(2b+1) y +1 & = 0 \\quad ... [2]\r\n\\end{align}\\]\r\n\\(a \\neq -\\dfrac{1}{4}\\) \u306a\u306e\u3067, [2] \u306f \\(y\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f\u3067\u3042\u308a, \u3053\u308c\u304c\u91cd\u89e3\u3092\u3082\u3064\u306e\u3067, \u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} = (2b+1)^2 -(4a+1) & = 0 \\\\\r\nb^2 +b -a & = 0 \\\\\r\n\\text{\u2234} \\quad a & = b(b+1)\r\n\\end{align}\\]\r\n\u305f\u3060\u3057, \\(a \\neq -\\dfrac{1}{4}\\) \u3088\u308a\r\n\\[\\begin{align}\r\nb^2 +b +\\dfrac{1}{4} & = \\left( b+\\dfrac{1}{2} \\right)^2 \\neq 0 \\\\\r\n\\text{\u2234} \\quad b & \\neq -\\dfrac{1}{2}\r\n\\end{align}\\]\r\n\u307e\u305f, \\(b = 0\\) \u306e\u5834\u5408\u306f\u9664\u304f\u306e\u3067\r\n\\[\r\n(a,b) \\neq (0,0)\r\n\\]\r\n\u4ee5\u4e0a\u3088\u308a, \\(a ,b\\) \u306e\u95a2\u4fc2\u306f\r\n\\[\r\n\\underline{a = b(b+1) \\ \\left( (a,b) \\neq (0,0) , \\left( -\\dfrac{1}{4} , -\\dfrac{1}{2} \\right) \\right)}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(C\\) \u306f<\/p>\r\n<ul>\r\n<li><p>\\(a \\gt 0\\) \u306e\u3068\u304d, \u6955\u5186<\/p><\/li>\r\n<li><p>\\(a = 0\\) \u306e\u3068\u304d, \u653e\u7269\u7dda<\/p><\/li>\r\n<li><p>\\(a \\lt 0\\) \u306e\u3068\u304d, \u53cc\u66f2\u7dda<\/p><\/li>\r\n<\/ul>\r\n<p>\u306a\u306e\u3067, <strong>(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} \\text{\u6955\u5186} : & b \\lt -1 , \\ 0 \\lt b \\\\ \\text{\u653e\u7269\u7dda} : & b = -1 \\\\ \\text{\u53cc\u66f2\u7dda} : & -1 \\lt b \\lt -\\dfrac{1}{2} , -\\dfrac{1}{2} \\lt b \\lt 0 \\end{array} \\right.}\r\n\\]\r\n<p><strong>(3)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u306e\u7d50\u679c\u3092 [2] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n(2b+1)^2 y^2+2(2b+1)y +1 & = 0 \\\\\r\n\\left\\{ (2b+1)y +1 \\right\\}^2 & = 0 \\\\\r\n\\text{\u2234} \\quad y = -\\dfrac{1}{2b+1} &\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \u70b9 P \u306e \\(y\\) \u5ea7\u6a19\u3067\u3042\u308a, \\(-1 \\lt b , 0 \\lt b\\) \u3067\u53d6\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u306f<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tsukuba_r_2007_06_01.png\" alt=\"tsukuba_r_2007_06_01\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\r\n-1 \\lt y \\lt 0 , \\ 0 \\lt y \\lt 1\r\n\\]\r\n\u3088\u3063\u3066, P \u306e\u8ecc\u8de1\u306f\r\n\\[\r\ny = 2x-1 \\quad ( -1 \\lt y \\lt 0 , 0 \\lt y \\lt 1 )\r\n\\]\r\n\u56f3\u793a\u3059\u308b\u3068\u4e0b\u56f3\u5b9f\u7dda\u90e8\uff08\u25cb\u306f\u9664\u304f\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tsukuba_r_2007_06_02.png\" alt=\"tsukuba_r_2007_06_02\" class=\"aligncenter size-full\" \/>\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u3067, \\(2\\) \u6b21\u66f2\u7dda \\(C : \\ x^2+ay^2+by = 0\\) \u304c\u76f4\u7dda \\(L : \\ y = 2x-1\\) \u306b\u70b9 P \u3067\u63a5\u3057\u3066\u3044\u308b. \u305f\u3060\u3057, \\(a \\neq -\\dfrac{1}{ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kbr200706\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[101],"tags":[144,109],"class_list":["post-705","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2007","tag-tsukuba_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/705","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=705"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/705\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}