{"id":28964,"date":"2021-04-28T13:00:22","date_gmt":"2021-04-28T13:00:22","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28964"},"modified":"2024-09-22T02:00:51","modified_gmt":"2024-09-22T02:00:51","slug":"%e6%a4%ad%e5%9c%86%e5%92%8c%e5%9c%86%e7%9a%84%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%a4%ad%e5%9c%86%e5%92%8c%e5%9c%86%e7%9a%84%e6%96%b9%e7%a8%8b\/","title":{"rendered":"\u692d\u5706\u548c\u5706\u7684\u65b9\u7a0b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u692d\u5706\u548c\u5706\u7684\u65b9\u7a0b<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n   \u672c\u8bfe\u89e3\u91ca\u4e86\u5982\u4f55\u6839\u636e\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49\u63a8\u5bfc\u692d\u5706\u7684\u65b9\u7a0b\uff0c\u8be5\u5b9a\u4e49\u89c4\u5b9a\u692d\u5706\u4e0a\u4efb\u610f\u4e00\u70b9\u5230\u4e24\u4e2a\u56fa\u5b9a\u7126\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u662f\u6052\u5b9a\u7684\u3002\u901a\u8fc7\u8be6\u7ec6\u7684\u4ee3\u6570\u63a8\u5bfc\uff0c\u5f97\u51fa\u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u53ca\u5176\u6807\u51c6\u5f62\u5f0f\uff0c\u5e76\u5c55\u793a\u692d\u5706\u4e0e\u5706\u7684\u5173\u7cfb\uff0c\u8868\u660e\u5f53\u692d\u5706\u7684\u4e24\u4e2a\u534a\u8f74\u76f8\u7b49\u65f6\uff0c\u5706\u662f\u692d\u5706\u7684\u7279\u6b8a\u60c5\u51b5\u3002<br \/>\n   <\/em><\/p>\n<p>   <strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n   \u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u63a8\u5bfc<\/strong>\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49\u65b9\u7a0b\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u692d\u5706\u65b9\u7a0b\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f\u3002<\/li>\n<\/ol>\n<p>   \u5185\u5bb9\u76ee\u5f55<br \/>\n   <a href=\"#1\">\u51e0\u4f55\u516c\u5f0f<\/a><br \/>\n   <a href=\"#2\">\u692d\u5706\u65b9\u7a0b\u7684\u63a8\u5bfc<\/a><br \/>\n   <a href=\"#3\">\u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b<\/a><br \/>\n   <a href=\"#4\">\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b<\/a><br \/>\n   <a href=\"#5\">\u5316\u7b80\u4e3a\u5706\u7684\u65b9\u7a0b<\/a>\n   <\/p>\n<p>   <\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/HHiC0bp-Vyc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><br \/>\n   <a name=\"1\"><\/a><\/p>\n<h2>\u51e0\u4f55\u516c\u5f0f<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=133s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e3a\u4e86\u5f97\u5230\u63cf\u8ff0\u692d\u5706\u7684\u65b9\u7a0b\uff0c<\/strong> <\/a> \u6211\u4eec\u5fc5\u987b\u50cf \u629b\u7269\u7ebf \u4e00\u6837\uff0c\u63a8\u7406\u692d\u5706\u7684\u51e0\u4f55\u610f\u4e49\u3002\u692d\u5706\u662f\u5e73\u9762\u4e0a\u6240\u6709\u70b9\u7684\u96c6\u5408\uff0c\u8fd9\u4e9b\u70b9\u5230\u4e24\u4e2a\u79f0\u4e3a\u7126\u70b9\u7684\u56fa\u5b9a\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u662f\u6052\u5b9a\u7684\u3002<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-rHroj77w4-o\/YIhoGfTvE_I\/AAAAAAAAFAw\/2Yoa3Q2yrmknQMPObDz8wuyDoOehCug5QCLcBGAsYHQ\/s0\/elipse.PNG\" alt=\"\u692d\u5706\" class=\" aligncenter lazyload\" width=\"338\" height=\"241\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-rHroj77w4-o\/YIhoGfTvE_I\/AAAAAAAAFAw\/2Yoa3Q2yrmknQMPObDz8wuyDoOehCug5QCLcBGAsYHQ\/s0\/elipse.PNG\" alt=\"\u692d\u5706\" class=\" aligncenter lazyload\" width=\"338\" height=\"241\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u5c06\u6ee1\u8db3\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d(f_1,p) + d(f_2,p) = \u5e38\u6570<\/span>\n<p>   <a name=\"2\"><\/a><\/p>\n<h2>\u692d\u5706\u65b9\u7a0b\u7684\u63a8\u5bfc<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=311s\" target=\"_blank\" rel=\"noopener\"><strong>\u6839\u636e\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49<\/strong><\/a>\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u63cf\u8ff0\u692d\u5706\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u3002\u4e3a\u4e86\u7b80\u5316\u63a8\u5bfc\uff0c\u6211\u4eec\u5047\u8bbe\u7126\u70b9\u4f4d\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">f_1 =(-c,0)<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">f_2 =(c,0),<\/span> \u6240\u4ee5\u4efb\u610f\u4e00\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">p=(x,y)<\/span> \u5728\u692d\u5706\u4e0a\u65f6\uff0c\u6ee1\u8db3\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2 + y^2} + \\sqrt{(x-c)^2 + y^2} = 2a<\/span>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-LtAamnh5D78\/YIiBshjM70I\/AAAAAAAAFA4\/hGiHx6jf_nMOOUHfH-Ywj34TyDJDGEv-wCLcBGAsYHQ\/s0\/ecuacion%2Bde%2Blas%2Belipses.PNG\" alt=\"\u692d\u5706\u65b9\u7a0b\" class=\" aligncenter lazyload\" width=\"412\" height=\"333\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-LtAamnh5D78\/YIiBshjM70I\/AAAAAAAAFA4\/hGiHx6jf_nMOOUHfH-Ywj34TyDJDGEv-wCLcBGAsYHQ\/s0\/ecuacion%2Bde%2Blas%2Belipses.PNG\" alt=\"\u692d\u5706\u65b9\u7a0b\" class=\" aligncenter lazyload\" width=\"412\" height=\"333\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u5176\u4e2d<span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u662f\u4e00\u4e2a\u56fa\u5b9a\u5e38\u6570\u3002\u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u5982\u4e0b\u63a8\u5bfc\uff1a<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2 + y^2} + \\sqrt{(x-c)^2 + y^2} = 2a<\/span><\/td>\n<td>; \u51e0\u4f55\u5b9a\u4e49\u7684\u692d\u5706<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x-c)^2 + y^2} = 2a - \\sqrt{(x+c)^2 + y^2}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(x-c)^2 + \\cancel{y^2} = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + (x+c)^2 + \\cancel{y^2}<\/span><\/td>\n<td>; \u5bf9(1)\u5e73\u65b9<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(x-c)^2 = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + (x+c)^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\cancel{x^2} -2xc + \\cancel{c^2} = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + \\cancel{x^2} +2xc + \\cancel{c^2} <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">-2xc = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} +2xc <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">4a \\sqrt{(x+c)^2 + y^2} = 4a^2 +4xc = 4(a^2 + xc) <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a \\sqrt{(x+c)^2 + y^2} = a^2 + xc <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a^2 [(x+c)^2 + y^2] = (a^2 + xc)^2 <\/span><\/td>\n<td>; \u5bf9(2)\u5e73\u65b9<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a^2 [x^2 + 2xc + c2 + y^2] = a^4 +2a^2xc + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> a^2 x^2 + \\cancel{2xca^2} + a^2 c2 + a^2 y^2 = a^4 + \\cancel{2a^2xc} + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> a^2 x^2 + a^2 c2 + a^2 y^2 = a^4 + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2 (a^2 - c^2) + a^2 y^2 = a^4 - a^2 c^2 =a^2(a^2-c^2) <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\dfrac{x^2}{a^2} +\\dfrac{ y^2}{a^2-c^2} = 1 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt a^2 - c^2 =: b^2 <\/span><\/td>\n<td>; \u56fe\u5f62\u663e\u793a<span class=\"katex-eq\" data-katex-display=\"false\">b^2<\/span>\u662f\u6b63\u6570\u3002<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{\\dfrac{x^2}{a^2} +\\dfrac{ y^2}{b^2} = 1}<\/span><\/td>\n<td>; \u6765\u81ea(3)\u548c(4)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\left(\\dfrac{x}{a}\\right)^2 + \\left(\\dfrac{y}{b}\\right)^2 = 1}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\">\u8fd9\u5c31\u662f\u6211\u4eec\u79f0\u4e3a\u201c\u692d\u5706\u65b9\u7a0b\u201d\u7684\u516c\u5f0f\u3002<\/p>\n<p>   <a name=\"3\"><\/a><\/p>\n<h2>\u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=706s\" target=\"_blank\" rel=\"noopener\"><strong>\u6211\u4eec\u521a\u521a\u5f97\u5230\u7684\u65b9\u7a0b<\/strong><\/a> \u53ef\u4ee5\u901a\u8fc7\u5e73\u79fb\u53d8\u6362\u63a8\u5bfc\u51fa\u5b83\u7684\u4e00\u822c\u5f62\u5f0f\uff0c\u8fdb\u884c\u66ff\u6362 <span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto (x-h)<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto (y-k).<\/span> \u4ece\u800c\u5f97\u5230\u692d\u5706\u65b9\u7a0b\u7684\u4e00\u822c\u5f62\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\left(\\dfrac{x-h}{a}\\right)^2 + \\left(\\dfrac{y-k}{b}\\right)^2 = 1}<\/span>\n<p style=\"text-align: justify;\">\u8fd9\u662f\u4e00\u4e2a\u4e2d\u5fc3\u5728\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span>\u7684\u692d\u5706<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-lkxt91FvMTs\/YIiQaL9wpII\/AAAAAAAAFBA\/sUxc6ajd6tcPymC8g4oh3M0l2CTI-xOvgCLcBGAsYHQ\/s0\/elipsegeneral.PNG\" alt=\"\u4e00\u822c\u692d\u5706\" class=\" aligncenter lazyload\" width=\"469\" height=\"373\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-lkxt91FvMTs\/YIiQaL9wpII\/AAAAAAAAFBA\/sUxc6ajd6tcPymC8g4oh3M0l2CTI-xOvgCLcBGAsYHQ\/s0\/elipsegeneral.PNG\" alt=\"\u4e00\u822c\u692d\u5706\" class=\" aligncenter lazyload\" width=\"469\" height=\"373\" \/><\/noscript><br \/>\n   <a name=\"4\"><\/a><\/p>\n<h2>\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=761s\" target=\"_blank\" rel=\"noopener\"><strong>\u901a\u8fc7\u4ee3\u6570\u8fd0\u7b97<\/strong><\/a>\u6211\u4eec\u5f97\u51fa\u4e86\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\dfrac{x-h}{a}\\right)^2 + \\left(\\dfrac{y-k}{b}\\right)^2 = 1<\/span><\/td>\n<td>; \u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 (x-h)^2 + a^2(y-k)^2 = a^2 b^2<\/span><\/td>\n<td>; \u5c06\u65b9\u7a0b\u4e58\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">a^2b^2<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 [x^2-2xh+h^2] + a^2[y^2-2yk + k^2] = a^2 b^2<\/span><\/td>\n<td>; \u5c55\u5f00\u5e73\u65b9<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2-2hb^2 x + h^2b^2 + a^2 y^2-2ka^2y + k^2a^2 = a^2 b^2<\/span><\/td>\n<td>; \u5c55\u5f00\u62ec\u53f7<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2- 2hb^2 x + a^2 y^2-2ka^2y +(h^2b^2 + k^2a^2 - a^2 b^2) = 0 <\/span><\/td>\n<td>; \u5408\u5e76\u5e38\u6570\u9879<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u5728\u6700\u540e\u7684\u8868\u8fbe\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u66ff\u6362 <span class=\"katex-eq\" data-katex-display=\"false\">A:=b^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">B:=-2hb^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">C:=a^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">D:=-2ka^2<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">E:=h^2b^2 + k^2a^2 - a^2 b^2.<\/span> \u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u692d\u5706\u65b9\u7a0b\u53ef\u4ee5\u88ab\u63cf\u8ff0\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Ax^2 + Bx + Cy^2 + Dy + E = 0<\/span>\n<p style=\"text-align: justify;\">\u8fd9\u5c31\u662f\u6211\u4eec\u79f0\u4e3a\u201c\u692d\u5706\u6807\u51c6\u65b9\u7a0b\u201d\u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<p style=\"text-align: justify;\">\u4ece\u8fd9\u4e9b\u63a8\u5bfc\u4e2d\uff0c\u53ef\u4ee5\u63d0\u53d6\u4e00\u4e9b\u5173\u4e8e\u6807\u51c6\u65b9\u7a0b\u5e38\u6570\u7684\u9650\u5236\u3002\u6700\u91cd\u8981\u7684\u662f <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u5fc5\u987b\u5177\u6709\u76f8\u540c\u7684\u7b26\u53f7\uff1b\u5426\u5219\uff0c\u6211\u4eec\u8ba8\u8bba\u7684\u5c06\u4e0d\u518d\u662f\u692d\u5706\uff0c\u800c\u662f\u53cc\u66f2\u7ebf\u3002\u5173\u4e8e\u6807\u51c6\u8868\u793a\u4e2d\u7684\u5e38\u6570\u8fd8\u6709\u66f4\u591a\u9650\u5236\uff0c\u4f46\u73b0\u5728\u8ba8\u8bba\u5b83\u4eec\u5e76\u4e0d\u9ad8\u6548\uff1b\u6211\u4eec\u5c06\u5728\u8be6\u7ec6\u8ba8\u8bba\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u7684\u8868\u5f81\u65f6\u8fdb\u4e00\u6b65\u63a2\u8ba8\u3002<\/p>\n<p>   <a name=\"5\"><\/a><\/p>\n<h2>\u5316\u7b80\u4e3a\u5706\u7684\u65b9\u7a0b<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=948s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u6211\u4eec\u8ba8\u8bba\u692d\u5706\u7684\u8868\u5f81\u65f6\uff0c\u6211\u4eec\u4f1a\u5ba1\u89c6<\/strong><\/a>\uff0c\u692d\u5706\u4e00\u822c\u65b9\u7a0b\u4e2d\u7684\u5e38\u6570<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u5bf9\u5e94\u4e8e\u692d\u5706\u7684\u534a\u8f74\u3002\u5982\u679c\u5c06\u4e24\u4e2a\u534a\u8f74\u76f8\u7b49\uff0c\u8bbe\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">a=b=r,<\/span> \u90a3\u4e48\u692d\u5706\u5c06\u8f6c\u5316\u4e3a\u534a\u5f84\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>\u7684\u5706\u3002<\/p>\n<h3>\u5706\u7684\u4e00\u822c\u65b9\u7a0b<\/h3>\n<p style=\"text-align: justify;\">\u7531\u6b64\u6211\u4eec\u5f97\u5230\u5706\u7684\u4e00\u822c\u65b9\u7a0b\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-h)^2 + (y-k)^2 = r^2<\/span>\n<h3>\u5706\u7684\u6807\u51c6\u65b9\u7a0b<\/h3>\n<p style=\"text-align: justify;\">\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u5f97\u5230\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Ax^2 + Bx + Cy^2 + Dy + E = 0<\/span>\n<p style=\"text-align: justify;\">\u5728\u5176\u6807\u51c6\u5f62\u5f0f\u4e2d\uff0c\u5706\u7684\u65b9\u7a0b\u4e0e\u692d\u5706\u65b9\u7a0b\u4e00\u81f4\uff0c\u56e0\u4e3a\u6211\u4eec\u5df2\u7ecf\u770b\u5230\uff0c\u5706\u662f\u692d\u5706\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u692d\u5706\u548c\u5706\u7684\u65b9\u7a0b \u6458\u8981\uff1a \u672c\u8bfe\u89e3\u91ca\u4e86\u5982\u4f55\u6839\u636e\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49\u63a8\u5bfc\u692d\u5706\u7684\u65b9\u7a0b\uff0c\u8be5\u5b9a\u4e49\u89c4\u5b9a\u692d\u5706\u4e0a\u4efb\u610f\u4e00\u70b9\u5230\u4e24\u4e2a\u56fa\u5b9a\u7126\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u662f\u6052\u5b9a\u7684\u3002\u901a\u8fc7\u8be6\u7ec6\u7684\u4ee3\u6570\u63a8\u5bfc\uff0c\u5f97\u51fa\u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u53ca\u5176\u6807\u51c6\u5f62\u5f0f\uff0c\u5e76\u5c55\u793a\u692d\u5706\u4e0e\u5706\u7684\u5173\u7cfb\uff0c\u8868\u660e\u5f53\u692d\u5706\u7684\u4e24\u4e2a\u534a\u8f74\u76f8\u7b49\u65f6\uff0c\u5706\u662f\u692d\u5706\u7684\u7279\u6b8a\u60c5\u51b5\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u63a8\u5bfc\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49\u65b9\u7a0b\u3002 \u8bc6\u522b\u692d\u5706\u65b9\u7a0b\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f\u3002 \u5185\u5bb9\u76ee\u5f55 \u51e0\u4f55\u516c\u5f0f \u692d\u5706\u65b9\u7a0b\u7684\u63a8\u5bfc \u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b \u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b \u5316\u7b80\u4e3a\u5706\u7684\u65b9\u7a0b \u51e0\u4f55\u516c\u5f0f \u4e3a\u4e86\u5f97\u5230\u63cf\u8ff0\u692d\u5706\u7684\u65b9\u7a0b\uff0c \u6211\u4eec\u5fc5\u987b\u50cf \u629b\u7269\u7ebf \u4e00\u6837\uff0c\u63a8\u7406\u692d\u5706\u7684\u51e0\u4f55\u610f\u4e49\u3002\u692d\u5706\u662f\u5e73\u9762\u4e0a\u6240\u6709\u70b9\u7684\u96c6\u5408\uff0c\u8fd9\u4e9b\u70b9\u5230\u4e24\u4e2a\u79f0\u4e3a\u7126\u70b9\u7684\u56fa\u5b9a\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u662f\u6052\u5b9a\u7684\u3002 \u4e5f\u5c31\u662f\u8bf4\uff0c\u5c06\u6ee1\u8db3\uff1a \u692d\u5706\u65b9\u7a0b\u7684\u63a8\u5bfc \u6839\u636e\u692d\u5706\u7684\u51e0\u4f55\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u63cf\u8ff0\u692d\u5706\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u3002\u4e3a\u4e86\u7b80\u5316\u63a8\u5bfc\uff0c\u6211\u4eec\u5047\u8bbe\u7126\u70b9\u4f4d\u4e8e \u548c \u6240\u4ee5\u4efb\u610f\u4e00\u70b9 \u5728\u692d\u5706\u4e0a\u65f6\uff0c\u6ee1\u8db3\uff1a \u5176\u4e2d \u662f\u4e00\u4e2a\u56fa\u5b9a\u5e38\u6570\u3002\u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u5982\u4e0b\u63a8\u5bfc\uff1a (1) ; \u51e0\u4f55\u5b9a\u4e49\u7684\u692d\u5706 (2) ; \u5bf9(1)\u5e73\u65b9 (3) ; \u5bf9(2)\u5e73\u65b9 (4) ; \u56fe\u5f62\u663e\u793a\u662f\u6b63\u6570\u3002 (5) ; \u6765\u81ea(3)\u548c(4) \u8fd9\u5c31\u662f\u6211\u4eec\u79f0\u4e3a\u201c\u692d\u5706\u65b9\u7a0b\u201d\u7684\u516c\u5f0f\u3002 \u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b \u6211\u4eec\u521a\u521a\u5f97\u5230\u7684\u65b9\u7a0b \u53ef\u4ee5\u901a\u8fc7\u5e73\u79fb\u53d8\u6362\u63a8\u5bfc\u51fa\u5b83\u7684\u4e00\u822c\u5f62\u5f0f\uff0c\u8fdb\u884c\u66ff\u6362 \u548c \u4ece\u800c\u5f97\u5230\u692d\u5706\u65b9\u7a0b\u7684\u4e00\u822c\u5f62\u5f0f\uff1a \u8fd9\u662f\u4e00\u4e2a\u4e2d\u5fc3\u5728\u70b9\u7684\u692d\u5706 \u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b \u901a\u8fc7\u4ee3\u6570\u8fd0\u7b97\u6211\u4eec\u5f97\u51fa\u4e86\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a (1) ; \u692d\u5706\u7684\u4e00\u822c\u65b9\u7a0b ; \u5c06\u65b9\u7a0b\u4e58\u4ee5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28959,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":39,"footnotes":""},"categories":[591,575],"tags":[],"class_list":["post-28964","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-591","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u692d\u5706\u548c\u5706\u7684\u65b9\u7a0b - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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