\u653e\u7269\u7dda \\(y=x^2\\) \u4e0a\u306b2\u70b9 P , Q \u304c\u3042\u308b. \u7dda\u5206 PQ \u306e\u4e2d\u70b9\u306e \\(y\\) \u5ea7\u6a19\u3092 \\(h\\) \u3068\u3059\u308b.<\/p>\r\n
(1)<\/strong>\u3000\u7dda\u5206 PQ \u306e\u9577\u3055 \\(L\\) \u3068\u50be\u304d \\(m\\) \u3067, \\(h\\) \u3067\u8868\u305b.<\/p><\/li>\r\n (2)<\/strong>\u3000\\(L\\) \u3092\u56fa\u5b9a\u3057\u305f\u3068\u304d, \\(h\\) \u304c\u3068\u308a\u3046\u308b\u5024\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n P , Q \u306e \\(x\\) \u5ea7\u6a19\u3092 \\(p , q\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nm & = \\dfrac{p^2-q^2}{p-q} = p+q , \\\\\r\nL & = \\sqrt{(p-q)^2 +(p^2-q^2)^2} \\\\\r\n& = \\sqrt{(p-q)^2 \\left\\{ (p+q)^2+1 \\right\\}} \\\\\r\n& = \\sqrt{\\left\\{ m^2 -4pq \\right\\} (m^2+1)} \\\\\r\n\\text{\u2234} \\quad & pq =\\dfrac{1}{4} \\left( m^2 -\\dfrac{L^2}{m^2+1} \\right)\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\nh & = \\dfrac{p^2+q^2}{2} \\\\\r\n& = \\dfrac{1}{2} \\left\\{ m^2 -\\dfrac{1}{2} \\left( m^2 -\\dfrac{L^2}{m^2+1} \\right) \\right\\} \\\\\r\n& = \\underline{\\dfrac{1}{4} \\left( m^2 +\\dfrac{L^2}{m^2+1} \\right)}\r\n\\end{align}\\]\r\n (2)<\/strong><\/p>\r\n \\(t =m^2+1\\) \u3068\u304a\u304f\u3068, \\(t \\geqq 1\\) .\r\n\\[\r\nh =\\dfrac{1}{4} \\left(t+\\dfrac{L^2}{t} -1 \\right)\r\n\\]\r\n\\(f(t) =h\\) \u3068\u304a\u304f\u3068<\/p>\r\n 1*<\/strong>\u3000\\(L \\geqq 1\\) \u306e\u3068\u304d 2*<\/strong>\u3000\\(0 \\lt L \\lt 1\\) \u306e\u3068\u304d\r\n\\[\r\nf'(t) =\\dfrac{1}{4} \\left( 1 -\\dfrac{L^2}{t^2} \\right) \\geqq 0\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(t)\\) \u306f\u5358\u8abf\u5897\u52a0\u3057\r\n\\[\r\nf(t) \\geqq f(1) =\\dfrac{L^2}{4}\r\n\\]\r\n\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} \\dfrac{L^2}{4} & \\ \\left( \\ 0 \\lt L \\lt 1 \\text{\u306e\u3068\u304d} \\right) \\\\ \\dfrac{2L-1}{4} & \\ \\left( \\ L \\geqq 1 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\r\n\\]<\/li>\r\n<\/ol>\r\n","protected":false},"excerpt":{"rendered":"\u653e\u7269\u7dda \\(y=x^2\\) \u4e0a\u306b2\u70b9 P , Q \u304c\u3042\u308b. \u7dda\u5206 PQ \u306e\u4e2d\u70b9\u306e \\(y\\) \u5ea7\u6a19\u3092 \\(h\\) \u3068\u3059\u308b. (1)\u3000\u7dda\u5206 PQ \u306e\u9577\u3055 \\(L\\) \u3068\u50be\u304d \\(m\\) \u3067, \\(h\\) \u3067\u8868\u305b. (2)\u3000 … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
\r\n
\r\n\u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\\begin{align}\r\nf(t) & = \\dfrac{1}{4} \\left( 2 \\sqrt{t \\cdot \\dfrac{L^2}{t}} -1 \\right) \\\\\r\n& = \\dfrac{2L-1}{4}\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(t =\\dfrac{L^2}{t}\\) \u3059\u306a\u308f\u3061 \\(t =L\\) \u306e\u3068\u304d<\/p><\/li>\r\n