(1)<\/strong>\u3000\u7dda\u5206 QR \u306e\u9577\u3055\u3092 \\(s\\) , \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n (2)<\/strong>\u3000QR \u306e\u9577\u3055\u304c \\(1\\) \u3067\u3042\u308b\u3088\u3046\u306b P \u304c\u52d5\u304f\u3068\u304d, P \u306e\u8ecc\u8de1\u3092\u6c42\u3081, \u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \u70b9 P \u3092\u901a\u308b\u50be\u304d \\(k\\) \u306e\u76f4\u7dda\u306e\u5f0f\u306f\r\n\\[\r\ny = k (x-s) +t\r\n\\]\r\n\u3053\u308c\u3092 \\(C\\) \u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\nx^2 +\\left\\{ k(x-s) +t \\right\\}^2 & = 1 \\\\\r\nx^2 +k^2(x-s)^2 +2kt(x-s) +t^2 -1 & = 0 \\\\\r\n\\text{\u2234} \\quad (k^2+1)x^2 +2k(t-ks)x +(t-ks)^2 -1 & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u91cd\u89e3\u3092\u3082\u3066\u3070\u3088\u3044\u306e\u3067, \u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} = k^2(t-ks)^2 -(k^2+1) \\left\\{ (t-ks)^2 -1 \\right\\} & = 0 \\\\\r\nk^2+1 -(t-ks)^2 & = 0 \\\\\r\n\\text{\u2234} \\quad (s^2-1) k^2 -2stk +t^2 -1 & = 0\r\n\\end{align}\\]\r\n\u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092 \\(k _ 1 , k _ 2 \\ ( k _ 1 \\lt k _ 2 )\\) \u3068\u304a\u304f\u3068, \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\nk _ 1 +k _ 2 = \\dfrac{2st}{s^2+1} , \\ k _ 1 k _ 2 = \\dfrac{t^2 -1}{s^2+1} \\quad ... [1]\r\n\\]\r\nQ , R \u306e \\(y\\) \u5ea7\u6a19\u306f, \\(k _ 1(1-s) +t , \\ k _ 2(1-s)+t\\) \u3068\u8868\u305b\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{QR} & = \\left\\{ k _ 1(1-s)+t \\right\\} -\\left\\{ k _ 2(1-s)+t \\right\\} \\\\\r\n& = | s-1 | ( k _ 2 -k _ 1 )\r\n\\end{align}\\]\r\n[1] \u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\text{QR} & = |s-1| \\sqrt{( k _ 1+k _ 2 )^2 -2 k _ 1 k _ 2} \\\\\r\n& = |s-1| \\sqrt{\\dfrac{4s^2t^2}{(s^2-1)^2} -\\dfrac{4(t^2-1)}{s^2-1}} \\\\\r\n& = \\dfrac{2|s-1|}{|s^2-1|} \\sqrt{s^2t^2 -(s^2-1)(t^2-1)} \\\\\r\n& = \\underline{\\dfrac{2 \\sqrt{s^2+t^2-1}}{|s+1|}}\r\n\\end{align}\\]\r\n (2)<\/strong><\/p>\r\n \\(\\text{QR} =1\\) \u306a\u306e\u3067, (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\\begin{align}\r\n2 \\sqrt{s^2+t^2-1} & = |s+1| \\\\\r\n\\text{\u2234} \\quad 4(s^2+t^2-1) = (s+1)^2 \\\\\r\n3s^2 -2s +4t^2 & = 5 \\\\\r\n3 \\left( s -\\dfrac{1}{3} \\right)^2 +4t^2 & = \\dfrac{16}{3} \\\\\r\n\\text{\u2234} \\quad \\dfrac{9 \\left( s -\\frac{1}{3} \\right)^2}{16} +\\dfrac{3 t^2}{4} & = 1\r\n\\end{align}\\]\r\n\u6761\u4ef6\u3088\u308a \\(s \\neq \\pm 1\\) \u306a\u306e\u3067, \u6c42\u3081\u308b\u8ecc\u8de1\u306f\r\n\\[\r\n\\underline{\\text{\u6955\u5186} : \\ \\dfrac{9 \\left( x -\\frac{1}{3} \\right)^2}{16} +\\dfrac{3 y^2}{4} = 1 \\quad ( s \\neq 1 )}\r\n\\]\r\n\u3053\u308c\u3092\u56f3\u793a\u3059\u308b\u3068, \u4e0b\u56f3\uff08\u25cb\u306f\u9664\u304f\uff09\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
![\"yokokoku_r_200904_01\"](\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/yokokoku_r_200904_01.png\")
\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306b\u5186 \\(C : \\ x^2+y^2 = 1\\) \u304c\u3042\u308b. \\(C\\) \u306e\u5916\u90e8\u306e\u70b9 P \\(( s, t ) \\ (s \\neq \\pm 1 )\\) \u304b\u3089 \\(C\\) \u3078\u5f15\u3044\u305f \\(2\\) \u3064\u306e\u63a5\u7dda\u3068 … \u7d9a\u304d\u3092\u8aad\u3080