{"id":11266,"date":"2022-11-26T17:07:51","date_gmt":"2022-11-26T08:07:51","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11266"},"modified":"2022-11-29T09:56:59","modified_gmt":"2022-11-29T00:56:59","slug":"orbit","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/orbit.html","title":{"rendered":"\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\uff1a\u5186\u3084\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3068\u9664\u5916\u70b9\u306e\u8a08\u7b97"},"content":{"rendered":"\n<p>\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u70b9\u306b\u3064\u3044\u3066\u3001\u70b9\u304c\u52d5\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u5b8c\u6210\u3055\u308c\u308b\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u70b9\u3068\u3044\u3046\u306e\u306f\u3001\u7279\u5b9a\u306e\u5ea7\u6a19\u306b\u3068\u3069\u307e\u3063\u3066\u3044\u308b\u3068\u306f\u9650\u3089\u305a\u3001\u52d5\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u70b9\u304c\u63cf\u304f\u8ecc\u9053\u3068\u3057\u3066\u306f\u3001\u76f4\u7dda\u3084\u653e\u7269\u7dda\u3001\u5186\u306a\u3069\u3055\u307e\u3056\u307e\u3067\u3059\u3002\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u624b\u9806\u304c\u3042\u308b\u305f\u3081\u3001\u5177\u4f53\u7684\u306a\u65b9\u6cd5\u3092\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u305f\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u9664\u5916\u70b9\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u6570\u5b66\u3067\u91cd\u8981\u306a\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u308b\u624b\u9806<\/h2>\n<p>\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7279\u5b9a\u306e\u56f3\u5f62\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u70b9\u304c\u52d5\u304f\u3068\u304d\u3001\u70b9\u306e\u8ecc\u9053\u3092\u65b9\u7a0b\u5f0f\u306b\u3088\u3063\u3066\u8868\u305b\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u308b\u3068\u304d\u3001\u6b63\u3057\u3044\u624b\u9806\u304c\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u8ecc\u9053\u306e\u8a08\u7b97\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u6c42\u3081\u305f\u3044\u8ecc\u9053\u306e\u5ea7\u6a19\u3092\\((x,y)\\)\u3068\u8868\u3059\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<p>\u6c42\u3081\u305f\u3044\u5ea7\u6a19\u4ee5\u5916\u306e\u70b9\u306b\u3064\u3044\u3066\u3082\u3001\u6587\u5b57\u3092\u5229\u7528\u3057\u3066\u8868\u3057\u305f\u3044\u30b1\u30fc\u30b9\u306f\u591a\u3044\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(x,y\\)\u4ee5\u5916\u306e\u6587\u5b57\u3092\u5229\u7528\u3057\u3066\u70b9\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u3070\u3001\\((a,b)\\)\u3084\\((s,t)\\)\u3068\u5ea7\u6a19\u3092\u8a2d\u5b9a\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u306e\u5f8c\u3001\\(a,b\\)\u3084\\(s,t\\)\u306a\u3069\u306e\u6587\u5b57\u3092\u6d88\u3059\u3068\u3001\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u5b9f\u969b\u306b\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3067\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u8ecc\u9053\u306b\u3088\u308b\u5186\u306e\u65b9\u7a0b\u5f0f\uff1a\u30a2\u30dd\u30ed\u30cb\u30a6\u30b9\u306e\u5186<\/h3>\n<p>2\u3064\u306e\u70b9\u306b\u3064\u3044\u3066\u3001\u8ddd\u96e2\u306e\u5272\u5408\u304c\u4e00\u5b9a\u306b\u306a\u308b\u3088\u3046\u306b\u65b0\u305f\u306a\u70b9\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u304d\u3001\u5f97\u3089\u308c\u308b\u8ecc\u9053\u3092\u30a2\u30dd\u30ed\u30cb\u30a6\u30b9\u306e\u5186\u3068\u3044\u3044\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>2\u70b9A\\((-2,0)\\)\u3068B\\((4,0)\\)\u304b\u3089\u306e\u8ddd\u96e2\u306e\u6bd4\u304c2:1\u3068\u306a\u308b\u70b9P\u306e\u8ecc\u9053\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u70b9P\u306e\u8ecc\u9053\u3092\\((x,y)\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u70b9A\u3068\u70b9B\u306b\u3064\u3044\u3066\u3001\u70b9P\u304b\u3089\u306e\u8ddd\u96e2\u306e\u6bd4\u304c2:1\u306b\u306a\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(AP:BP=2:1\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/dkfj1.jpg\" alt=\"\" width=\"408\" height=\"290\" class=\"aligncenter size-full wp-image-11362\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(AP=2BP\\)<\/p>\n<p>\\(AP^2=4BP^2\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((x+2)^2+y^2=4(x-4)^2+4y^2\\)<\/p>\n<p>\\(x^2+4x+4=4(x^2-8x+16)+3y^2\\)<\/p>\n<p>\\(3x^2+3y^2-36x+60=0\\)<\/p>\n<p>\\(x^2+y^2-12x+20=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9P\u306b\u3088\u308b\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u91cd\u5fc3\u306e\u8ecc\u9053\u3068\u9664\u5916\u70b9<\/h3>\n<p>\u306a\u304a\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001<span style=\"color: #ff0000;\">\u9664\u5916\u70b9<\/span>\u306e\u5b58\u5728\u3092\u8a8d\u8b58\u3057\u307e\u3057\u3087\u3046\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u9664\u5916\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u70b9\u304c\u5b58\u5728\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u3068\u304d\u306b\u9664\u5916\u70b9\u3092\u8003\u616e\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5b9f\u969b\u306b\u554f\u984c\u3092\u89e3\u3044\u3066\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u70b9A\\((3,0)\\)\u3068\u70b9B\\((0,3)\\)\u306b\u52a0\u3048\u3001\u5186\\(x^2+y^2=9\\)\u4e0a\u3092\u52d5\u304f\u70b9P\u306e3\u3064\u3092\u9802\u70b9\u3068\u3059\u308b\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3G\u306e\u8ecc\u9053\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u70b9P\u306f\u52d5\u304f\u305f\u3081\u3001\u91cd\u5fc3G\u3082\u52d5\u304d\u307e\u3059\u3002\u6c42\u3081\u305f\u3044\u8ecc\u9053\u306f\u70b9G\u3067\u3059\u3002\u305d\u3053\u3067\u70b9G\u306e\u5ea7\u6a19\u3092\\((x,y)\\)\u3001\u70b9P\u306e\u5ea7\u6a19\u3092\\((a,b)\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u70b9P\u306f\u5186\\(x^2+y^2=9\\)\u306e\u4e0a\u3092\u52d5\u304f\u305f\u3081\u3001\\(a^2+b^2=9\\)\u3067\u3059\u3002\u307e\u305f\u70b9G\u306f\u91cd\u5fc3\u3067\u3042\u308b\u305f\u3081\u3001\\(x\\)\u5ea7\u6a19\u3068\\(y\\)\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{3+0+a}{3}\\)<\/li>\n<li>\\(y\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{0+3+b}{3}\\)<\/li>\n<\/ul>\n<p>\\(x=\\displaystyle\\frac{3+a}{3}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=3x-3\\)\u3067\u3059\u3002\u307e\u305f\\(y=\\displaystyle\\frac{3+b}{3}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(b=3y-3\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(a^2+b^2=9\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a^2+b^2=9\\)<\/p>\n<p>\\((3x-3)^2+(3y-3)^2=9\\)<\/p>\n<p>\\((x-1)^2+(y-1)^2=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u591a\u304f\u306e\u4eba\u306f\\((x-1)^2+(y-1)^2=1\\)\u304c\u6b63\u89e3\u3068\u8003\u3048\u307e\u3059\u3002\u305f\u3060\u3001\u3053\u306e\u72b6\u614b\u3067\u306f\u4e0d\u5b8c\u5168\u3067\u3059\u3002\u306a\u305c\u3001\\((x-1)^2+(y-1)^2=1\\)\u304c\u7b54\u3048\u3067\u306f\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u305d\u308c\u306f\u3001\u9664\u5916\u70b9\u3092\u8003\u616e\u3057\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u56f3\u3092\u4f5c\u3063\u3066\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/dghr15.jpg\" alt=\"\" width=\"389\" height=\"320\" class=\"aligncenter size-full wp-image-11274\" \/><\/p>\n<p><span style=\"color: #0000ff;\">AB\u4e0a\u306e\u70b9\u3067\u306f\u3001\u4e09\u89d2\u5f62\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/span>\u3064\u307e\u308a\u3001\u91cd\u5fc3\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u76f4\u7ddaAB\u3068\u5186\\((x-1)^2+(y-1)^2=1\\)\u306e\u4ea4\u70b9\u306f\u9664\u5916\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u56f3\u3088\u308a\u3001\u76f4\u7ddaAB\u306e\u65b9\u7a0b\u5f0f\u306f\\(y=-x+3\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u76f4\u7ddaAB\u3068\u5186\\((x-1)^2+(y-1)^2=1\\)\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((x-1)^2+(y-1)^2=1\\)<\/p>\n<p>\\((x-1)^2+(-x+2)^2=1\\)<\/p>\n<p>\\(2x^2-6x+4=0\\)<\/p>\n<p>\\(x^2-3x+2=0\\)<\/p>\n<p>\\((x-2)(x-1)=0\\)<\/p>\n<p>\\(x=1,2\\)\u306e\u3068\u304d\u3001\u5186\u3068\u76f4\u7dda\u306f\u4ea4\u308f\u308a\u307e\u3059\u3002\u305d\u3053\u3067\\(y\\)\u5ea7\u6a19\u3082\u8a08\u7b97\u3059\u308b\u3068\u3001\\((1,2)\\)\u3068\\((2,1)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\\((1,2)\\)\u3068\\((2,1)\\)\u306e\u5ea7\u6a19\u3067\u306f\u3001\u4e09\u89d2\u5f62\u3092\u4f5c\u308c\u306a\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b54\u3048\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5186\\((x-1)^2+(y-1)^2=1\\)\u3001\u305f\u3060\u3057\u70b9\\((1,2)\\)\u3068\u70b9\\((2,1)\\)\u3092\u9664\u304f\u3002<\/li>\n<\/ul>\n<p>\u8ecc\u9053\u306e\u554f\u984c\u3092\u89e3\u304f\u5834\u5408\u3001\u56f3\u3092\u63cf\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u70b9\u304c\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u304b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3068\u304d\u3001\u9664\u5916\u70b9\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u6c17\u3092\u4ed8\u3051\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<h2>\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u30fb\u7dda\u5bfe\u79f0\u306a\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f<\/h2>\n<p>\u5148\u307b\u3069\u3001\u5186\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002\u305d\u308c\u3067\u306f\u3001\u8ecc\u9053\u304c\u76f4\u7dda\u3092\u63cf\u304f\u5834\u5408\u306f\u3069\u306e\u3088\u3046\u306b\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5148\u307b\u3069\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u65b9\u7a0b\u5f0f\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u4f8b\u984c\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>2\u3064\u306e\u76f4\u7dda\\(2x+y-3=0\\)\u3068\\(x-2y+1=0\\)\u306e\u306a\u3059\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u307e\u305a\u3001\u6c42\u3081\u308b\u8ecc\u9053\u3092\u70b9P\\((x,y)\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u89d2\u306e\u4e8c\u7b49\u5206\u7dda\u3067\u306f\u3001\u70b9\u30682\u3064\u306e\u76f4\u7dda\u306f\u5fc5\u305a\u7b49\u8ddd\u96e2\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u70b9\u3068\u76f4\u7dda\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8ecc\u9053\u306e\u8a08\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{|2x+y-3|}{\\sqrt{2^2+1^2}}=\\displaystyle\\frac{|x-2y+1|}{\\sqrt{1^2+(-2)^2}}\\)<\/p>\n<p>\\(\\displaystyle\\frac{|2x+y-3|}{\\sqrt{5}}=\\displaystyle\\frac{|x-2y+1|}{\\sqrt{5}}\\)<\/p>\n<p>\\(|2x+y-3|=|x-2y+1|\\)<\/p>\n<p>\\(2x+y-3=\u00b1(x-2y+1)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u306f\\(x+3y-4=0\\)\u3068\\(3x-y-2=0\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/eqjh1.jpg\" alt=\"\" width=\"600\" height=\"282\" class=\"aligncenter size-full wp-image-11283\" \/><\/p>\n<p>\u4ed6\u306e\u8ecc\u9053\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306b\u3064\u3044\u3066\u3082\u3001\u540c\u69d8\u306b\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u8ecc\u9053\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u76f4\u7dda\\(y=2x\\)\u3092\u57fa\u6e96\u306b\u3057\u3066\u3001\u76f4\u7dda\\(3x+y=15\\)\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u6c42\u3081\u308b\u76f4\u7dda\u4e0a\u306e\u5ea7\u6a19\u3092\u70b9P\\((x,y)\\)\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u76f4\u7dda\\(3x+y=15\\)\u4e0a\u306e\u70b9Q\u3092\\((a,b)\\)\u3068\u3059\u308b\u3068\u3001\\(3a+b=15\\)\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(b=-3a+15\\)\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u3001\u70b9P\u3068\u70b9Q\u306e\u4e2d\u70b9\u306f\u305d\u308c\u305e\u308c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{x+a}{2}\\)<\/li>\n<li>\\(y\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{y+b}{2}\\)<\/li>\n<\/ul>\n<p>\\(y=2x\\)\u3092\u57fa\u6e96\u306b\u3057\u3066\u70b9P\u3068\u70b9Q\u306f\u7dda\u5bfe\u79f0\u3067\u3042\u308b\u305f\u3081\u3001\u70b9P\u3068\u70b9Q\u306e\u4e2d\u70b9\u306f\u76f4\u7dda\\(y=2x\\)\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{y+b}{2}=2\u00d7\\displaystyle\\frac{x+a}{2}\\)<\/p>\n<p>\\(y+b=2x+2a\\)<\/p>\n<p>\\(b=-3a+15\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(y+(-3a+15)=2x+2a\\)<\/p>\n<p>\\(2x-y=-5a+15\\) &#8211; \u2460<\/p>\n<p>\u307e\u305f\u7dda\u5bfe\u79f0\u306e\u6027\u8cea\u3088\u308a\u3001\u76f4\u7ddaPQ\u306f\\(y=2x\\)\u306b\u5bfe\u3057\u3066\u5782\u76f4\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(2\u00d7\\displaystyle\\frac{y-b}{x-a}=-1\\)<\/p>\n<p>\\(2y-2b=a-x\\)<\/p>\n<p>\\(2y-2(-3a+15)=a-x\\)<\/p>\n<p>\\(x+2y=-5a+30\\) &#8211; \u2461<\/p>\n<p>\\(\u2460-\u2461\\)\u3088\u308a\u3001<\/p>\n<p>\\(x-3y=-15\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/dkfj2.jpg\" alt=\"\" width=\"600\" height=\"322\" class=\"aligncenter size-full wp-image-11364\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(x-3y=-15\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u6c42\u3081\u308b\u5ea7\u6a19\u3092\\((x,y)\\)\u3068\u8a2d\u5b9a\u3059\u308b\u3068\u304d\u3001\\((a,b)\\)\u3084\\((s,t)\\)\u306a\u3069\u3001\u305d\u306e\u4ed6\u306e\u5ea7\u6a19\u306b\u95a2\u3059\u308b\u6587\u5b57\u3092\u6d88\u3059\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>2\u76f4\u7dda\u306e\u4ea4\u70b9\u306e\u8ecc\u9053\u3068\u9664\u5916\u70b9<\/h3>\n<p>\u6b21\u306b\u30012\u3064\u306e\u76f4\u7dda\u306b\u3088\u3063\u3066\u4f5c\u3089\u308c\u308b\u4ea4\u70b9\u306e\u8ecc\u9053\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>2\u3064\u306e\u76f4\u7dda\\(y=ax-a-2\\)\u3068\\(y=bx+3b\\)\u306f\u4e92\u3044\u306b\u5782\u76f4\u3092\u4fdd\u3061\u3001\u5e73\u9762\u4e0a\u3092\u52d5\u3044\u3066\u3044\u307e\u3059\u3002\\(a,b\\)\u304c\u5b9f\u6570\u3067\u3042\u308b\u3068\u304d\u30012\u3064\u306e\u76f4\u7dda\u306b\u3088\u308b\u4ea4\u70b9P\u306e\u8ecc\u9053\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>2\u3064\u306e\u76f4\u7dda\u306f\u5782\u76f4\u3067\u3042\u308b\u305f\u3081\u3001\\(ab=-1\\)\u3067\u3059\u3002\u307e\u305f\u70b9P\u306e\u5ea7\u6a19\u3092\\((x,y)\\)\u3068\u3059\u308b\u3068\u3001\u70b9P\u306f\\(y=ax-a-2\\)\u3068\\(y=bx+3b\\)\u306e\u4e21\u65b9\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\\(ab=-1\\)\u3088\u308a\u3001\\(b=-\\displaystyle\\frac{1}{a}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(y=bx+3b\\)<\/p>\n<p>\\(y=-\\displaystyle\\frac{x}{a}-\\displaystyle\\frac{3}{a}\\)<\/p>\n<p>\\(ay=-x-3\\)<\/p>\n<p>\\(a=\\displaystyle\\frac{-x-3}{y}\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\\(a=\\displaystyle\\frac{-x-3}{y}\\)\u3092\\(y=ax-a-2\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(y=ax-a-2\\)<\/p>\n<p>\\(y=a(x-1)-2\\)<\/p>\n<p>\\(y=\\displaystyle\\frac{-x-3}{y}(x-1)-2\\)<\/p>\n<p>\\(y^2=-(x+3)(x-1)-2y\\)<\/p>\n<p>\\(y^2=-(x^2+2x-3)-2y\\)<\/p>\n<p>\\(x^2+y^2+2x+2y-3=0\\)<\/p>\n<p>\u305f\u3060\u3001\u7b54\u3048\u304c\\(x^2+y^2+2x+2y-3=0\\)\u3067\u306f\u4e0d\u5341\u5206\u3067\u3059\u3002\u9664\u5916\u70b9\u3092\u8003\u616e\u3057\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u56f3\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\\(x^2+y^2+2x+2y-3=0\\)\u3092\u5909\u5f62\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(x^2+y^2+2x+2y-3=0\\)<\/p>\n<p>\\((x+1)^2+(y+1)^2=5\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\((-1,-1)\\)\u304c\u4e2d\u5fc3\u3067\u3042\u308a\u3001\u534a\u5f84\\(\\sqrt{5}\\)\u306e\u5186\u8ecc\u9053\u3092\u63cf\u304f\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u6b21\u306b\\(y=ax-a-2\\)\u3092\u5909\u5f62\u3059\u308b\u3068\u3001\\(a(x-1)-2-y=0\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(y=ax-a-2\\)\u306f\u5fc5\u305a\\((1,-2)\\)\u3092\u901a\u308a\u307e\u3059\u3002\u305f\u3060\\(a\\)\u306e\u5024\u304c\u4f55\u3067\u3042\u3063\u3066\u3082\u3001\\(x=1\\)\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u3089\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u70b9P\u306f\\((1,0)\\)\u3092\u901a\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u307e\u305f\\(y=bx+3b\\)\u3092\u5909\u5f62\u3059\u308b\u3068\u3001\\(b(x+3)-y=0\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(y=bx+3b\\)\u306f\u5fc5\u305a\\((-3,0)\\)\u3092\u901a\u308a\u307e\u3059\u3002\u305f\u3060\\(b\\)\u306e\u5024\u304c\u4f55\u3067\u3042\u3063\u3066\u3082\u3001\\(x=-3\\)\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u3089\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u70b9P\u306f\\((-3,-2)\\)\u3092\u901a\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/eqjh2.jpg\" alt=\"\" width=\"600\" height=\"285\" class=\"aligncenter size-full wp-image-11285\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u304c\u7b54\u3048\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x^2+y^2+2x+2y-3=0\\)\u3001\u305f\u3060\u3057\u70b9\\((1,0)\\)\u3068\u70b9\\((-3,-2)\\)\u3092\u9664\u304f<\/li>\n<\/ul>\n<p>\u3053\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u3001\u9664\u5916\u70b9\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u6c17\u304c\u4ed8\u304f\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u56f3\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f0f\u304c\u6761\u4ef6\u3092\u6e80\u305f\u3059\u304b\u3069\u3046\u304b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u653e\u7269\u7dda\u3068\u76f4\u7dda\u306b\u3088\u308b\u5f26\u306e\u4e2d\u70b9\u306e\u8ecc\u9053<\/h3>\n<p>\u6b21\u306b\u653e\u7269\u7dda\u3068\u76f4\u7dda\u3092\u5229\u7528\u3059\u308b\u8ecc\u9053\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u653e\u7269\u7dda\\(y=x^2\\)\u3068\u76f4\u7dda\\(y=m(x+1)\\)\u304c\u7570\u306a\u308b2\u70b9A,B\u3067\u4ea4\u308f\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<ol>\n<li>\\(m\\)\u306e\u7bc4\u56f2\u306f\u3044\u304f\u3089\u3067\u3059\u304b\u3002<\/li>\n<li>\u7dda\u5206AB\u306e\u4e2d\u70b9\u306e\u8ecc\u9053\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ol>\n<p><strong>1) \\(m\\)\u306e\u7bc4\u56f2\u306f\u3044\u304f\u3089\u3067\u3059\u304b<\/strong><\/p>\n<p>\u4ea4\u70b9\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u3001\\(y=x^2\\)\u3092\\(y=m(x+1)\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(y=m(x+1)\\)<\/p>\n<p>\\(x^2=m(x+1)\\)<\/p>\n<p>\\(x^2-mx-m=0\\)<\/p>\n<p>\u653e\u7269\u7dda\\(y=x^2\\)\u3068\u76f4\u7dda\\(y=m(x+1)\\)\u304c\u7570\u306a\u308b2\u70b9\u3067\u4ea4\u308f\u308b\u305f\u3081\u306b\u306f\u3001\\(x^2-mx-m=0\\)\u304c2\u3064\u306e\u89e3\u3092\u3082\u3064\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u5224\u5225\u5f0f\\(D\\)\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\\(m\\)\u306e\u7bc4\u56f2\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\((-m)^2-4\u00d7-m&gt;0\\)<\/p>\n<p>\\(m^2+4m&gt;0\\)<\/p>\n<p>\\(m(m+4)&gt;0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(m&lt;-4,0&lt;m\\)\u304c\u7b54\u3048\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>2) \u7dda\u5206AB\u306e\u4e2d\u70b9\u306e\u8ecc\u9053\u3092\u6c42\u3081\u307e\u3057\u3087\u3046<\/strong><\/p>\n<p>\\(x^2-mx-m=0\\)\u306e\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001\u4e2d\u70b9\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u89e3\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3082\u3044\u3044\u3067\u3059\u304c\u3001\u8a08\u7b97\u3092\u7c21\u5358\u306b\u3059\u308b\u305f\u3081\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u30022\u3064\u306e\u89e3\u3092\\(\u03b1,\u03b2\\)\u3068\u3059\u308b\u3068\u3001\u4e2d\u70b9\u306f\\(\\displaystyle\\frac{\u03b1+\u03b2}{2}\\)\u3067\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u7dda\u5206AB\u306e\u4e2d\u70b9P\u306e\u5ea7\u6a19\u3092\\((x,y)\\)\u3068\u3059\u308b\u3068\u3001\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\u3001\\(x\\)\u5ea7\u6a19\u306f\\(\\displaystyle\\frac{m}{2}\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\\(x=\\displaystyle\\frac{m}{2}\\)\u3067\u3042\u308a\u3001\\(m=2x\\)\u306e\u3068\u304d\u3001\u7dda\u5206AB\u306e\u4e2d\u70b9\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u70b9P\u306f\\(y=m(x+1)\\)\u4e0a\u306b\u3042\u308b\u70b9\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(m=2x\\)\u3092\\(y=m(x+1)\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(y=m(x+1)\\)<\/p>\n<p>\\(y=2x(x+1)\\)<\/p>\n<p>\\(y=2x^2+2x\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x\\)\u5ea7\u6a19\u304c\u7dda\u5206AB\u306e\u4e2d\u70b9\u3067\u3042\u308b\\(\\displaystyle\\frac{m}{2}\\)\u306e\u3068\u304d\u3001\\(y=2x^2+2x\\)\u3068\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u6b21\u306b\u3001\\(x\\)\u306e\u7bc4\u56f2\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\\(m=2x\\)\u3068\\(m&lt;-4,0&lt;m\\)\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(m&lt;-4,0&lt;m\\)<\/p>\n<p>\\(2x&lt;-4,0&lt;2x\\)<\/p>\n<p>\\(x&lt;-2,0&lt;x\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7dda\u5206AB\u306e\u8ecc\u9053\u306f\u300c\\(y=2x^2+2x\\)\u306b\u3064\u3044\u3066\u3001\\(x&lt;-2,0&lt;x\\)\u306e\u90e8\u5206\u300d\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/eqjh3.jpg\" alt=\"\" width=\"561\" height=\"283\" class=\"aligncenter size-full wp-image-11286\" 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\u70b9\u3068\u3044\u3046\u306e\u306f\u3001\u7279\u5b9a\u306e\u5ea7\u6a19\u306b\u3068\u3069\u307e\u3063\u3066\u3044\u308b\u3068\u306f\u9650\u3089\u305a\u3001\u52d5\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u70b9\u304c\u63cf\u304f\u8ecc\u9053\u3068\u3057\u3066 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11287,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-11266","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=11266"}],"version-history":[{"count":11,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11266\/revisions"}],"predecessor-version":[{"id":11367,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/11266\/revisions\/11367"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/11287"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=11266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=11266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=11266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}