\u539f\u70b9\u3092 O \u3068\u3059\u308b \\(xy\\) \u5e73\u9762\u4e0a\u306b, \\(2\\) \u76f4\u7dda\r\n\\[\\begin{align}\r\n\\ell _ 1 & : \\ y =mx \\\\\r\n\\ell _ 2 & : \\ y = -mx\r\n\\end{align}\\]\r\n\u304c\u3042\u308b.\r\n\u305f\u3060\u3057, \\(m \\gt 1\\) \u3068\u3059\u308b. \\(\\ell _ 1\\) \u4e0a\u306b\u70b9 P \\(( s, ms )\\) , \\(\\ell _ 2\\) \u4e0a\u306b\u70b9 Q \\(( t, -mt )\\) \u3092 \\(s \\neq 0 , \\ t \\neq 0\\) \u3068\u306a\u308b\u3088\u3046\u306b\u3068\u308b.\r\nP \u3092\u901a\u308a \\(\\ell _ 1\\) \u306b\u5782\u76f4\u306a\u76f4\u7dda\u3068, Q \u3092\u901a\u308a \\(\\ell _ 2\\) \u306b\u5782\u76f4\u306a\u76f4\u7dda\u306e\u4ea4\u70b9\u3092 R \u3068\u3059\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n
(1)<\/strong>\u3000R \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n (2)<\/strong>\u3000PQ \u3068 OR \u304c\u5e73\u884c\u3068\u306a\u308b\u3088\u3046\u306b, P , Q \u3092\u52d5\u304b\u3059\u3068\u304d, R \u306e\u8ecc\u8de1\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \\[\\begin{align}\r\n\\ell _ 1 & : \\ y = -\\dfrac{1}{m} (x-s) +ms = -\\dfrac{x}{m} +\\dfrac{s}{m} +ms , \\\\\r\n\\ell _ 2 & : \\ y = \\dfrac{1}{m} (x-t) -mt = \\dfrac{x}{m} -\\dfrac{t}{m} -mt\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \\(2\\) \u5f0f\u304b\u3089 \\(y\\) \u3092\u6d88\u53bb\u3057\u3066, \u4e21\u8fba \\(m\\) \u500d\u3059\u308b\u3068\r\n\\[\\begin{gather}\r\n-x +s +m^2s = x -t -m^2t \\\\\r\n\\text{\u2234} \\quad x = \\dfrac{(s+t)(m^2+1)}{2}\r\n\\end{gather}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\ny & = \\dfrac{s+t}{2} \\left( m+\\dfrac{1}{m} \\right) -\\dfrac{t}{m} -mt \\\\\r\n& = \\dfrac{(s-t)(m^2+1)}{2m}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, R \u306e\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{(s+t)(m^2+1)}{2} , \\dfrac{(s-t)(m^2+1)}{2m} \\right)}\r\n\\]\r\n (2)<\/strong><\/p>\r\n R \\((X, Y)\\) \u3068\u304a\u304f\u3068, (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\nX = \\dfrac{(s+t)(m^2+1)}{2} , \\ Y =\\dfrac{(s-t)(m^2+1)}{2m} \\quad ... [1]\r\n\\]\r\nPQ \u306e\u50be\u304d\u306f\r\n\\[\r\n\\dfrac{ms+mt}{s-t} = \\dfrac{m(s+t)}{s-t}\r\n\\]\r\nOR \u306e\u50be\u304d\u306f\r\n\\[\r\n\\dfrac{\\frac{s-t}{m}}{s+t} = \\dfrac{s-t}{m(s+t)}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\dfrac{m(s+t)}{s-t} & = \\dfrac{s-t}{m(s+t)} \\\\\r\nm^2 (s+t)^2 & = (s-t)^2 \\\\\r\n(s+t)^2 & = \\dfrac{(s-t)^2}{m^2}\r\n\\end{align}\\]\r\n\u4e21\u8fba\u3092 \\(\\dfrac{m^2+1}{4}\\) \u500d\u3059\u308c\u3070, [1] \u3088\u308a\r\n\\[\\begin{gather}\r\nX^2 = Y^2 \\\\\r\n\\text{\u2234} \\quad (X+Y)(X-Y) = 0\r\n\\end{gather}\\]\r\n\\(s \\neq 0\\) , \\(t \\neq 0\\) \u3088\u308a, \\(X \\neq 0\\) \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308c\u3070, \u6c42\u3081\u308b\u8ecc\u8de1\u306f\r\n\\[\r\n\\underline{\\text{\u76f4\u7dda} : \\ y = \\pm x \\quad ( \\text{\u305f\u3060\u3057, \u70b9} (0,0) \\text{\u3092\u9664\u304f} )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u539f\u70b9\u3092 O \u3068\u3059\u308b \\(xy\\) \u5e73\u9762\u4e0a\u306b, \\(2\\) \u76f4\u7dda \\[\\begin{align} \\ell _ 1 & : \\ y =mx \\\\ \\ell _ 2 & : \\ y = -mx \\end{align}\\] \u304c … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n