\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9\r\n\\[\r\n\\text{P} \\left( 0 , -\\sqrt{2} \\right) , \\ \\text{Q} \\left( 0 , \\sqrt{2} \\right) , \\ \\text{A} \\left( a , \\sqrt{a^2+1} \\right) \\quad ( 0 \\leqq a \\leqq 1 )\r\n\\]\r\n\u3092\u8003\u3048\u308b.<\/p>\r\n
(1)<\/strong>\u3000\\(2\\) \u3064\u306e\u7dda\u5206\u306e\u9577\u3055\u306e\u5dee \\(\\text{PA} -\\text{AQ}\\) \u306f \\(a\\) \u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057, \u305d\u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n (2)<\/strong>\u3000Q\u3092\u7aef\u70b9\u3068\u3057A\u3092\u901a\u308b\u534a\u76f4\u7dda\u3068\u653e\u7269\u7dda \\(y = \\dfrac{\\sqrt{2}}{8} x^2\\) \u3068\u306e\u4ea4\u70b9\u3092B\u3068\u3059\u308b. \u70b9B\u304b\u3089\u76f4\u7dda \\(y=2\\) \u3078\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068\u76f4\u7dda \\(y=2\\) \u3068\u306e\u4ea4\u70b9\u3092C\u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u7dda\u5206\u306e\u9577\u3055\u306e\u548c\r\n\\[\r\n\\text{PA} +\\text{AB} +\\text{BC}\r\n\\]\r\n\u306f \\(a\\) \u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057, \u305d\u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \\[\\begin{align}\r\n\\text{PA} & = \\sqrt{a^2 +\\left( \\sqrt{a^2 +1} +\\sqrt{2} \\right)^2} \\\\\r\n& = \\sqrt{2a^2 +3 +2 \\sqrt{2 \\left( a^2 +1 \\right)}} \\\\\r\n& = \\sqrt{\\left( \\sqrt{a^2 +1} +\\sqrt{2} \\right)^2} \\\\\r\n& = \\sqrt{a^2 +1} +\\sqrt{2}\r\n\\end{align}\\]\r\n\u540c\u69d8\u306b\u8003\u3048\u308b\u3068\r\n\\[\r\n\\text{AQ} = \\sqrt{a^2 +1} -\\sqrt{2}\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{PA} -\\text{AQ} = 2 \\sqrt{2} = ( \\text{\u4e00\u5b9a} )\r\n\\]\r\n (2)<\/strong><\/p>\r\n B \\(\\left( t , \\dfrac{\\sqrt{2} t^2}{8} \\right)\\) \u3068\u304a\u3051\u308b.\r\n\\[\r\n\\text{BC} = 2 -\\dfrac{\\sqrt{2} t^2}{8} \\quad ... [1]\r\n\\]\r\n\u76f4\u7dda AQ \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = \\dfrac{\\sqrt{a^2 +1} -\\sqrt{2}}{a} x +\\sqrt{2} \\\\\r\n& = \\dfrac{\\text{AQ}}{a} x +\\sqrt{2}\r\n\\end{align}\\]\r\n\\(\\text{AQ} : \\text{QB} = a : t\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{AB} & = \\dfrac{t-a}{a} \\text{AQ} \\\\\r\n& = \\left( \\dfrac{t}{a} -1 \\right) \\text{AQ} \\quad ... [2]\r\n\\end{align}\\]\r\nB \u306f AQ \u4e0a\u306e\u70b9\u306a\u306e\u3067\r\n\\[\r\n\\dfrac{\\sqrt{2} t^2}{8} = \\dfrac{\\text{AQ}}{a} t +\\sqrt{2}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u3068\u3042\u308f\u305b\u3066\r\n\\[\r\n\\text{BC} = 2 -\\left( \\dfrac{t}{a} \\text{AQ} +\\sqrt{2} \\right) \\quad ... [3]\r\n\\]\r\n[2] [3] \u3068 (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\text{PA} +\\text{AB} +\\text{BC} & = \\text{PA} -\\text{AQ} +2 -\\sqrt{2} \\\\\r\n& = \\underline{\\sqrt{2} +2} = ( \\text{\u4e00\u5b9a} )\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9 \\[ \\text{P} \\left( 0 , -\\sqrt{2} \\right) , \\ \\text{Q} \\left( 0 , \\sqrt{2} \\right) , \\ \\text{A} … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n