{"id":11798,"date":"2022-12-22T22:12:42","date_gmt":"2022-12-22T13:12:42","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11798"},"modified":"2022-12-26T05:05:55","modified_gmt":"2022-12-25T20:05:55","slug":"vector-7","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/vector-7.html","title":{"rendered":"\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\uff1a\u516c\u5f0f\u3068\u65b9\u7a0b\u5f0f\u306e\u95a2\u4fc2\u3001\u63a5\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f"},"content":{"rendered":"\n<p>\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5186\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u5186\u306e\u65b9\u7a0b\u5f0f\u3060\u3051\u3067\u306a\u304f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u5186\u3092\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3059\u65b9\u6cd5\u306f\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u65b9\u6cd5\u3092\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3089\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5186\u306e\u65b9\u7a0b\u5f0f\u3078\u5909\u63db\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\u63a5\u7dda\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3082\u3001\u5186\u3067\u5229\u7528\u3055\u308c\u308b\u6027\u8cea\u3092\u7528\u3044\u3066\u63a5\u7dda\u306b\u95a2\u308f\u308b\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u307e\u305f\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u70b9C\u304c\u5186\u306e\u4e2d\u5fc3\u3067\u3042\u308a\u3001\u70b9P\u306e\u4f4d\u7f6e\u304c\u5186\u5468\u4e0a\u306e\u5834\u5408\u3001\\(\\overrightarrow{CP}\\)\u3068\u8a18\u3059\u3053\u3068\u3067\u5186\u306e\u4e2d\u5fc3C\u304b\u3089\u5186\u5468\u4e0a\u307e\u3067\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8a18\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001CP\u306e\u9577\u3055\u306f\u534a\u5f84\\(r\\)\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7dda\u5206CP\u306e\u9577\u3055\u3092\u8868\u3059\\(|\\overrightarrow{CP}|\\)\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(|\\overrightarrow{CP}|=r\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u5229\u7528\u3059\u308b\u3068\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(|\\overrightarrow{p}-\\overrightarrow{c}|=r\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/mdf3.jpg\" alt=\"\" width=\"516\" height=\"216\" class=\"aligncenter size-full wp-image-11801\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3057\u305f\u3002<span style=\"color: #0000ff;\">\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u3069\u306e\u3088\u3046\u306b\u5c0e\u304d\u51fa\u305b\u308b\u306e\u304b\u5b66\u3079\u3070\u3001\u516c\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span>\u56f3\u5f62\u3092\u5229\u7528\u3057\u3066\u516c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u6b21\u306b\u3001\u4e21\u8fba\u3092\u4e8c\u4e57\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(|\\overrightarrow{p}-\\overrightarrow{c}|^2=r^2\\)<\/p>\n<p>\\((\\overrightarrow{p}-\\overrightarrow{c})^2=r^2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u30012\u3064\u76ee\u306e\u516c\u5f0f\u3067\u3042\u308b\\((\\overrightarrow{p}-\\overrightarrow{c})^2=r^2\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u4e8c\u4e57\u3059\u308b\u3060\u3051\u3067\u3042\u308b\u305f\u3081\u3001\u7c21\u5358\u306b\u516c\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u70b9C\uff08\\(\\overrightarrow{c}\\)\uff09\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84\\(r\\)\u306e\u5186\u306b\u3064\u3044\u3066\u3001\u4efb\u610f\u306e\u70b9\u3092P\uff08\\(\\overrightarrow{p}\\)\uff09\u3068\u3059\u308b\u3068\u304d\u3001\\(|3\\overrightarrow{p}-\\overrightarrow{c}|=6\\)\u306f\u3069\u306e\u3088\u3046\u306a\u5186\u3067\u3057\u3087\u3046\u304b\u3002<\/li>\n<\/ul>\n<p>\\(\\overrightarrow{p}\\)\u306f\u4e2d\u5fc3\u304b\u3089\u306e\u8ddd\u96e2\u3092\u8868\u3057\u3001\u57fa\u6e96\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\\(\\overrightarrow{p}\\)\u306e\u4fc2\u6570\u30921\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\left|\\overrightarrow{p}-\\displaystyle\\frac{1}{3}\\overrightarrow{c}\\right|=2\\)<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u56f3\u3067\u7dda\u5206OC\u3092\\(\\displaystyle\\frac{1}{3}\\)\u500d\u3057\u305f\u5834\u6240\u304c\u4e2d\u5fc3\u3067\u3042\u308a\u3001\u534a\u5f842\u306e\u5186\u3067\u3042\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\/12\/mdf4.jpg\" alt=\"\" width=\"212\" height=\"207\" class=\"aligncenter size-full wp-image-11802\" \/><\/p>\n<p>\u70b9C\u306e\u5834\u6240\u306b\u3088\u3063\u3066\u3001\u5186\u306e\u5834\u6240\u306f\u5909\u5316\u3057\u307e\u3059\u3002\u305f\u3060\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5186\u306e\u6027\u8cea\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5186\u306e\u65b9\u7a0b\u5f0f\u306b\u5909\u63db\u3059\u308b<\/h3>\n<p>\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306f\u5186\u306e\u65b9\u7a0b\u5f0f\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u4e00\u3064\u306e\u5186\u306b\u3064\u3044\u3066\u3001\u5186\u306e\u65b9\u7a0b\u5f0f\u3067\u3082\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u3082\u8868\u73fe\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/span><\/p>\n<p>\u4e2d\u5fc3C\u306e\u5ea7\u6a19\u3092\\((a,b)\\)\u3001\u70b9P\u306e\u5ea7\u6a19\u3092\\((x,y)\\)\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(\\overrightarrow{CP}=\\overrightarrow{p}-\\overrightarrow{c}\\)\u3092\u6210\u5206\u3067\u8868\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u6210\u5206\uff1a\\((x-a)\\)<\/li>\n<li>\\(y\\)\u6210\u5206\uff1a\\((y-b)\\)<\/li>\n<\/ul>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\((\\overrightarrow{p}-\\overrightarrow{c})^2=r^2\\)<\/p>\n<p>\\((x-a,y-b)^2=r^2\\)<\/p>\n<p>\\((x-a)^2+(y-b)^2=r^2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u5186\u306e\u65b9\u7a0b\u5f0f\u3068\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u3069\u3061\u3089\u3092\u5229\u7528\u3059\u308b\u307b\u3046\u304c\u6700\u9069\u306a\u306e\u304b\u306f\u554f\u984c\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3068\u5186\u306e\u65b9\u7a0b\u5f0f\u306e\u5909\u63db\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u306f\u91cd\u8981\u3067\u3059\u3002<\/p>\n<h3>\u76f4\u5f84\u306e\u4e21\u7aef\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u306a\u304a\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u76f4\u5f84\u306e\u4e21\u7aef\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u5186\u306e\u4e2d\u5fc3\u3092\u901a\u308b\u76f4\u7dda\uff08\u76f4\u5f84\uff09\u306b\u3064\u3044\u3066\u3001\u4e21\u7aef\u306e\u70b9\u3092\u305d\u308c\u305e\u308cA\uff08\\(\\overrightarrow{a}\\)\uff09\u3001B\uff08\\(\\overrightarrow{b}\\)\uff09\u3068\u3057\u307e\u3059\u3002\u5186\u5468\u4e0a\u306e\u4efb\u610f\u306e\u70b9\u3092P\uff08\\(\\overrightarrow{p}\\)\uff09\u3068\u3059\u308b\u3068\u3001<span style=\"color: #ff0000;\">AP\u3068BP\u306f\u5782\u76f4\u3067\u3042\u308b\u305f\u3081\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p>\\(\\overrightarrow{AP}\u00b7\\overrightarrow{BP}=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\((\\overrightarrow{p}-\\overrightarrow{a})\u00b7(\\overrightarrow{p}-\\overrightarrow{b})=0\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/mdf6.jpg\" alt=\"\" width=\"535\" height=\"251\" class=\"aligncenter size-full wp-image-11806\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3057\u305f\u3002\u3053\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u3082\u899a\u3048\u308b\u5fc5\u8981\u306f\u306a\u304f\u3001\u3069\u306e\u3088\u3046\u306b\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u4f5c\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4f8b\u984c\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>2\u70b9\\((2,3)\\)\u3001\\((4,1)\\)\u304c\u76f4\u5f84\u306e\u4e21\u7aef\u3067\u3042\u308b\u3068\u304d\u3001\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u306a\u304f\u3066\u3082\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3001\u3053\u3053\u3067\u306f\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u5186\u5468\u4e0a\u306e\u70b9\u3092P\\((x,y)\\)\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{AP}=\\overrightarrow{p}-\\overrightarrow{a}=(x-2,y-3)\\)<\/li>\n<li>\\(\\overrightarrow{BP}=\\overrightarrow{p}-\\overrightarrow{b}=(x-4,y-1)\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\overrightarrow{AP}\u00b7\\overrightarrow{BP}=0\\)<\/p>\n<p>\\((\\overrightarrow{p}-\\overrightarrow{a})\u00b7(\\overrightarrow{p}-\\overrightarrow{b})=0\\)<\/p>\n<p>\\((x-2)(x-4)+(y-3)(y-1)=0\\)<\/p>\n<p>\\((x^2-6x+8)+(y^2-4y+3)=0\\)<\/p>\n<p>\\((x-3)^2+(y-2)^2=2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5186\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u5186\u306e\u63a5\u7dda\u3068\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f<\/h2>\n<p>\u5186\u3067\u306f\u63a5\u7dda\u306b\u95a2\u3059\u308b\u554f\u984c\u3082\u3072\u3093\u3071\u3093\u306b\u51fa\u984c\u3055\u308c\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u5186\u306e\u63a5\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5186\u306e\u4e2d\u5fc3\u3092C\uff08\\(\\overrightarrow{c}\\)\uff09\u3001\u63a5\u7dda\u3068\u306e\u5186\u5468\u4e0a\u306e\u63a5\u70b9\u3092P<sub>0<\/sub>\uff08\\(\\overrightarrow{p_0}\\)\uff09\u3001\u63a5\u7dda\u4e0a\u306e\u4efb\u610f\u306e\u70b9\u3092P\uff08\\(\\overrightarrow{p}\\)\uff09\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(\\overrightarrow{CP_0}\u00b7\\overrightarrow{P_0P}\\)\\(=0\\)\u3068\u306a\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{CP_0}\u00b7\\overrightarrow{P_0P}=(\\overrightarrow{p_0}-\\overrightarrow{c})\u00b7(\\overrightarrow{p}-\\overrightarrow{p_0})\\)\\(=0\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/mdf8.jpg\" alt=\"\" width=\"360\" height=\"260\" class=\"aligncenter size-full wp-image-11808\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u63a5\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p>\u6b21\u306b\u3001\u5186\u306e\u63a5\u7dda\u3092\u307b\u304b\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3067\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u306e\u6761\u4ef6\u306b\u52a0\u3048\u3066\u3001\u534a\u5f84\u3092\\(r\\)\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u89d2\u5ea6\\(\u03b8\\)\u3092\u52a0\u3048\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/mdf9.jpg\" alt=\"\" width=\"371\" height=\"262\" class=\"aligncenter size-full wp-image-11809\" \/><\/p>\n<p>\u4e0a\u56f3\u3088\u308a\u3001\\(|\\overrightarrow{CP}|cos\u03b8=|\\overrightarrow{CP_0}|\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4e21\u8fba\u306b\\(|\\overrightarrow{CP_0}|\\)\u3092\u304b\u3051\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(|\\overrightarrow{CP}||\\overrightarrow{CP_0}|cos\u03b8=|\\overrightarrow{CP_0}|^2\\)<\/li>\n<\/ul>\n<p>\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u306e\u516c\u5f0f\u3088\u308a\u3001\\(\\overrightarrow{CP}\u00b7\\overrightarrow{CP_0}=|\\overrightarrow{CP}||\\overrightarrow{CP_0}|cos\u03b8\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u3092\u4ee3\u5165\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(|\\overrightarrow{CP}||\\overrightarrow{CP_0}|cos\u03b8=|\\overrightarrow{CP_0}|^2\\)<\/p>\n<p>\\(\\overrightarrow{CP}\u00b7\\overrightarrow{CP_0}=|\\overrightarrow{CP_0}|^2\\)<\/p>\n<p>\\((\\overrightarrow{p}-\\overrightarrow{c})\u00b7(\\overrightarrow{p_0}-\\overrightarrow{c})=|\\overrightarrow{CP_0}|^2\\)<\/p>\n<p>\u306a\u304a\\(|\\overrightarrow{CP_0}|\\)\u306f\u534a\u5f84\\(r\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\((\\overrightarrow{p}-\\overrightarrow{c})\u00b7(\\overrightarrow{p_0}-\\overrightarrow{c})=r^2\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u63a5\u7dda\u306b\u95a2\u3059\u308b2\u3064\u76ee\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u304b\u3089\u3001\u5186\u306e\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306b\u95a2\u3059\u308b\u516c\u5f0f\u3092\u5c0e\u51fa\u3059\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u5186\u306e\u63a5\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u3001\u5186\u306e\u63a5\u7dda\u3092\u5f97\u308b\u65b9\u7a0b\u5f0f\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u306b\u5206\u3051\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5186\u306e\u63a5\u7dda\u306e\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u63a5\u70b9P<sub>0<\/sub>\u3092\\(\\overrightarrow{p_0}=(x_0,y_0)\\)\u3001\u63a5\u7dda\u4e0a\u306e\u70b9P\u3092\\(\\overrightarrow{p}=(x,y)\\)\u3001\u4e2d\u5fc3C\u3092\\(\\overrightarrow{c}=(a,b)\\)\u3068\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\overrightarrow{p}-\\overrightarrow{c}=(x-a,y-b)\\)<\/li>\n<li>\\(\\overrightarrow{p_0}-\\overrightarrow{c}=(x_0-a,y_0-b)\\)<\/li>\n<\/ul>\n<p>\u524d\u8ff0\u306e\u3068\u304a\u308a\u3001\\((\\overrightarrow{p}-\\overrightarrow{c})\u00b7(\\overrightarrow{p_0}-\\overrightarrow{c})=r^2\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\\(x\\)\u6210\u5206\u3001\\(y\\)\u6210\u5206\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\((x-a)(x_0-a)+(y-b)(y_0-b)\\)\\(=r^2\\)<\/li>\n<\/ul>\n<p>\u3053\u3046\u3057\u3066\u3001\u5186\u306e\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u53c2\u8003\u307e\u3067\u306b\u3001\u4e2d\u5fc3\u304c\u539f\u70b9\u306e\u3068\u304d\u306f\\(\\overrightarrow{c}=(0,0)\\)\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(xx_0+yy_0=r^2\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u5186\u306e\u63a5\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5186\u306e\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u5f97\u308b\u305f\u3081\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b<\/h2>\n<p>\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3060\u3051\u3067\u306a\u304f\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3092\u899a\u3048\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u305f\u3060\u76f4\u7dda\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u3088\u308a\u3082\u3001\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306e\u307b\u3046\u304c\u516c\u5f0f\u306e\u4f5c\u308a\u65b9\u306f\u7c21\u5358\u3067\u3059\u3002\u516c\u5f0f\u306e\u6697\u8a18\u306f\u610f\u5473\u304c\u306a\u304f\u3001\u56f3\u5f62\u3092\u5229\u7528\u3057\u3066\u516c\u5f0f\u3092\u4f5c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5186\u306e\u30d9\u30af\u30c8\u30eb\u65b9\u7a0b\u5f0f\u306b\u306f\u4e3b\u306b2\u7a2e\u985e\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u4e2d\u5fc3\u3084\u534a\u5f84\u304c\u308f\u304b\u3063\u3066\u3044\u306a\u304f\u3066\u3082\u3001\u76f4\u5f84\u306e\u4e21\u7a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