{"id":1403,"date":"2017-03-10T21:46:11","date_gmt":"2017-03-10T12:46:11","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1403"},"modified":"2021-09-23T22:43:10","modified_gmt":"2021-09-23T13:43:10","slug":"tok201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201603\/","title":{"rendered":"\u6771\u5de5\u59272016\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u6c34\u5e73\u306a\u5e73\u9762 \\(\\alpha\\) \u306e\u4e0a\u306b\u534a\u5f84 \\(r _ 1\\) \u306e\u7403 \\(S _ 1\\) \u3068\u534a\u5f84 \\(r _ 2\\) \u306e\u7403 \\(S _ 2\\) \u304c\u4e57\u3063\u3066\u304a\u308a, \\(S _ 1\\) \u3068 \\(S _ 2\\) \u306f\u5916\u63a5\u3057\u3066\u3044\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(S _ 1 , S _ 2\\) \u304c \\(\\alpha\\) \u3068\u63a5\u3059\u308b\u70b9\u3092\u305d\u308c\u305e\u308c \\(\\text{P} _ 1 , \\text{P} _ 2\\) \u3068\u3059\u308b. \u7dda\u5206 \\(\\text{P} _ 1 \\text{P} _ 2\\) \u306e\u9577\u3055\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\alpha\\) \u306e\u4e0a\u306b\u4e57\u3063\u3066\u304a\u308a, \\(S _ 1\\) \u3068 \\(S _ 2\\) \u306e\u4e21\u65b9\u306b\u5916\u63a5\u3057\u3066\u3044\u308b\u7403\u3059\u3079\u3066\u3092\u8003\u3048\u308b. \u305d\u308c\u3089\u306e\u7403\u3068 \\(\\alpha\\) \u306e\u63a5\u70b9\u306f, \\(1\\) \u3064\u306e\u5186\u306e\u4e0a\u307e\u305f\u306f \\(1\\) \u3064\u306e\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n\"\"\r\n

    \\(r _ 1 \\neq r _ 2\\) \u306e\u3068\u304d, \\(S _ 1 , S _ 2\\) \u306e\u4e2d\u5fc3\u3092\u7d50\u3076\u7dda\u5206\u3092\u659c\u8fba\u3068\u3059\u308b\u76f4\u89d2\u4e09\u89d2\u5f62\u306b\u7740\u76ee\u3057\u3066\r\n\\[\\begin{align}\r\n\\text{P} _ 1 \\text{P} _ 2 & = \\sqrt{( r _ 1 +r _ 2 )^2 -| r _ 1 -r _ 2 |^2} \\\\\r\n& = 2 \\sqrt{r _ 1 r _ 2} \\quad ... [1]\r\n\\end{align}\\]\r\n\\(r _ 1 = r _ 2\\) \u306e\u3068\u304d, \\(\\text{P} _ 1 \\text{P} _ 2 = 2 r _ 1\\) \u3067\u3042\u308a, [1] \u3067\u6e80\u305f\u3055\u308c\u3066\u3044\u308b.
    \r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{P} _ 1 \\text{P} _ 2 = \\underline{2 \\sqrt{r _ 1 r _ 2}}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(S _ 1 , S _ 2\\) \u4e21\u65b9\u306b\u5916\u63a5\u3059\u308b\u5186\u3092 \\(S _ 3\\) \u3068\u3057, \\(S _ 3\\) \u306e\u534a\u5f84\u3092 \\(r _ 3\\) , \\(\\alpha\\) \u3068\u306e\u63a5\u70b9\u3092 \\(\\text{P} _ 3\\) \u3068\u304a\u304f.
    \r\n(1)<\/strong> \u306e\u7d50\u679c\u304b\u3089\r\n\\[\r\n\\text{P} _ 1 \\text{P} _ 3 = 2 \\sqrt{r _ 1 r _ 3} , \\ \\text{P} _ 2 \\text{P} _ 3 = 2 \\sqrt{r _ 2 r _ 3} \\quad ... [2]\r\n\\]\r\n\\(\\text{P} _ 1 \\ ( 0, 0 )\\) , \\(\\text{P} _ 2 \\ ( 2 \\sqrt{ r _ 1 r _ 2 }, 0 )\\) \u3068\u306a\u308b\u3088\u3046\u306b, \\(xy\\) \u5ea7\u6a19\u3092\u5b9a\u3081, \\(\\text{P} _ 3 \\ ( X, Y )\\) \u3068\u304a\u304f\u3068, [2] \u3088\u308a\r\n\\[\\begin{align}\r\nX^2 +Y^2 & = 4 r _ 1 r _ 3 \\quad ... [3] \\\\\r\n( X -2 \\sqrt{ r _ 1 r _ 2 } )^2 +Y^2 & = 4 r _ 2 r _ 3 \\quad ... [4]\r\n\\end{align}\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(r _ 1 = r _ 2\\) \u306e\u3068\u304d
      \r\n\\([3] -[4]\\) \u3088\u308a\r\n\\[\\begin{align}\r\n4 r _ 1 X -4 {r _ 1}^2 & = 0 \\\\\r\n\\text{\u2234} \\quad X & = r _ 1\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \u76f4\u7dda\u3092\u8868\u3059.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(r _ 1 \\neq r _ 2\\) \u306e\u3068\u304d
      \r\n\\([3] \\times r _ 2 -[4] \\times r _ 1\\) \u3088\u308a\r\n\\[\\begin{align}\r\nr _ 2 X^2 +r _ 2 Y^2 & = r _ 1 ( X -2 \\sqrt{ r _ 1 r _ 2 } )^2 +r _ 1 Y^2 \\\\\r\n( r _ 2 -r _ 1 ) X^2 +4 r _ 1 \\sqrt{ r _ 1 r _ 2 } X & +( r _ 2 -r _ 1 ) Y^2 = 4 {r _ 1}^2 r _ 2 \\\\\r\n\\left( X +\\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 +Y^2 & = \\dfrac{4 {r _ 1}^2 r _ 2}{r _ 2 -r _ 1} +\\left( \\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 \\\\\r\n\\text{\u2234} \\quad \\left( X +\\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 +Y^2 & = \\left( \\dfrac{2 r _ 1 r _ 2}{r _ 2 -r _ 1} \\right)^2\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \u5186\u3092\u8868\u3059.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u6c34\u5e73\u306a\u5e73\u9762 \\(\\alpha\\) \u306e\u4e0a\u306b\u534a\u5f84 \\(r _ 1\\) \u306e\u7403 \\(S _ 1\\) \u3068\u534a\u5f84 \\(r _ 2\\) \u306e\u7403 \\(S _ 2\\) \u304c\u4e57\u3063\u3066\u304a\u308a, \\(S _ 1\\) \u3068 \\(S _ 2\\) \u306f\u5916\u63a5\u3057\u3066\u3044\u308b … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[153],"tags":[141,162],"class_list":["post-1403","post","type-post","status-publish","format-standard","hentry","category-toko_2016","tag-toko","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1403","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1403"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1403\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}