\r\n \r\n
\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
(1)<\/strong><\/p>\r\n\u70b9 P \\(\\left( t , \\dfrac{t^2}{4} \\right)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\n\\text{PQ}^2 = \\left( t -2a \\right)^2 +\\left( \\dfrac{t^2}{4} +\\dfrac{a^2}{4} -2 \\right)^2\r\n\\]\r\n\u3053\u308c\u3092 \\(f(t) \\ ( t \\gt 0 )\\) \u3068\u3057\u3066, \\(t\\) \u3067\u5fae\u5206\u3059\u308b\u3068\r\n\\[\\begin{align}\r\nf'(t) & = 2 ( t -2a ) +2 \\left( \\dfrac{t^2}{4} -\\dfrac{a^2}{4} -2 \\right) \\cdot \\dfrac{t}{2} \\\\\r\n& = \\dfrac{t^3}{4} +\\left( 4 -\\dfrac{a^2}{4} \\right) t -4a \\\\\r\n& = \\dfrac{1}{4} (t-a) \\underline{( t^2 +at +16 )} _ {[1]}\r\n\\end{align}\\]\r\n\\([1] = 0\\) \u306e\u5224\u5225\u5f0f\u3092 \\(D\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nD = a^2 -64 = (a+8)(a-8)\r\n\\]\r\n
\r\n1*<\/strong>\u3000\\(0 \\lt a \\leqq 8\\) \u306e\u3068\u304d
\r\n\\([1] \\leqq 0\\) \u306a\u306e\u3067, \\(f(t) = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\nt = a\r\n\\]\r\n\u3086\u3048\u306b, \\(f(t)\\) \u306e\u5897\u6e1b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccc} t & (0) & \\cdots & a & \\cdots \\\\ \\hline f'(t) & & - & 0 & + \\\\ \\hline f(t) & & \\searrow & \\text{\u6700\u5c0f} & \\nearrow \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6700\u5c0f\u5024\u306f\r\n\\[\r\nf(a) = a^2 +4\r\n\\]<\/li>\r\n2*<\/strong>\u3000\\(a \\gt 8\\) \u306e\u3068\u304d
\r\n\\(f(t) = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\nt = a , \\ \\dfrac{a +\\sqrt{a^2 -64}}{2}\r\n\\]\r\n\u3086\u3048\u306b, \\(f(t)\\) \u306e\u5897\u6e1b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccccc} t & (0) & \\cdots & \\dfrac{a +\\sqrt{a^2 -64}}{2} & \\cdots & a & \\cdots \\\\ \\hline f'(t) & & + & 0 & - & 0 & + \\\\ \\hline f(t) & & \\nearrow & \\text{\u6975\u5927} & \\searrow & \\text{\u6975\u5c0f} & \\nearrow \\end{array}\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\\begin{align}\r\nf(0) -f(a) & = 4a^2 +\\left( \\dfrac{a^2}{4} -2 \\right)^2 -( a^2 +4 ) \\\\\r\n& = 3 a^2 +\\left( \\dfrac{a^2}{4} -2 \\right)^2 +4 \\gt 0\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u6700\u5c0f\u5024\u306f\r\n\\[\r\nf(a) = a^2 +4\r\n\\]<\/li>\r\n<\/ol>\r\n\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{\\sqrt{a^2 +4}}\r\n\\]\r\n
(2)<\/strong><\/p>\r\n\u5186 \\(C _ 2\\) \u306f, \u70b9 Q \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(\\sqrt{2} a\\) \u306e\u5186\u3067\u3042\u308b.
\r\nPQ \u306e\u6700\u5c0f\u5024\u3068, \u5186 \\(C _ 2\\) \u306e\u534a\u5f84\u306e\u5927\u5c0f\u3067\u5834\u5408\u5206\u3051\u3057\u3066\u8003\u3048\u308b.\r\n\\[\r\n2 a^2 -( a^2 +4 ) = a^2 -4 = (a+2)(a-2)\r\n\\]\r\n\u306a\u306e\u3067<\/p>\r\n
\r\n1*<\/strong>\u3000\\(\\sqrt{a^2 +4} \\gt \\sqrt{2} a\\) \u3059\u306a\u308f\u3061 \\(0 \\lt a \\lt 2\\) \u306e\u3068\u304d
\r\n\\(C _ 1\\) \u3068 \\(C _ 2\\) \u306f\u5171\u6709\u70b9\u3092\u3082\u305f\u305a, \u70b9 R \u304c, \u7dda\u5206 PQ \u3068 \\(C _ 2\\) \u306e\u4ea4\u70b9\u3068\u306a\u308b\u3068\u304d\u306b, PR \u306f\u6700\u5c0f\u3068\u306a\u308a, \u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\sqrt{a^2 +4} -\\sqrt{2} a\r\n\\]\r\n![\"\"](\"https:\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tok20160101.svg\")
<\/li>\r\n2*<\/strong>\u3000\\(\\sqrt{a^2 +4} \\leqq \\sqrt{2} a\\) \u3059\u306a\u308f\u3061 \\(a \\geqq 2\\) \u306e\u3068\u304d
\r\n\\(C _ 1\\) \u3068 \\(C _ 2\\) \u306f\u5171\u6709\u70b9\u3092\u3082\u3064\u306e\u3067, PR \u306e\u6700\u5c0f\u5024\u306f\r\n\\[\r\n0\r\n\\]\r\n![\"\"](\"https:\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tok20160102.svg\")
<\/li>\r\n<\/ol>\r\n\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} \\sqrt{a^2 +4} -\\sqrt{2} a & ( \\ 0 \\lt a \\lt 2 \\text{\u306e\u3068\u304d} \\ ) \\\\ 0 & ( \\ a \\geqq 2 \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n\r\n
\r\n « \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n <\/p>\r\n <\/div>","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u6b63\u306e\u5b9a\u6570\u3068\u3057, \u653e\u7269\u7dda \\(y = \\dfrac{x^2}{4}\\) \u3092 \\(C _ 1\\) \u3068\u3059\u308b. (1)\u3000\u70b9 P \u304c \\(C _ 1\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d, P \u3068\u70b9 Q \\(\\left( 2a , \\d […]","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":[153],"tags":[141,162],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1397"}],"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=1397"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1397\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}