{"id":29025,"date":"2021-05-05T13:00:46","date_gmt":"2021-05-05T13:00:46","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29025"},"modified":"2024-09-22T04:31:58","modified_gmt":"2024-09-22T04:31:58","slug":"%e5%9c%86%e9%94%a5%e6%9b%b2%e7%ba%bf-%e6%8a%9b%e7%89%a9%e7%ba%bf-%e6%a4%ad%e5%9c%86-%e5%8f%8c%e6%9b%b2%e7%ba%bf%e7%9a%84%e7%89%b9%e5%be%81%e4%b8%8e%e5%9b%be%e5%bd%a2","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%9c%86%e9%94%a5%e6%9b%b2%e7%ba%bf-%e6%8a%9b%e7%89%a9%e7%ba%bf-%e6%a4%ad%e5%9c%86-%e5%8f%8c%e6%9b%b2%e7%ba%bf%e7%9a%84%e7%89%b9%e5%be%81%e4%b8%8e%e5%9b%be%e5%bd%a2\/","title":{"rendered":"\u5706\u9525\u66f2\u7ebf: \u629b\u7269\u7ebf, \u692d\u5706, \u53cc\u66f2\u7ebf\u7684\u7279\u5f81\u4e0e\u56fe\u5f62"},"content":{"rendered":"<p><center><\/p>\n<h1>\u5706\u9525\u66f2\u7ebf: \u629b\u7269\u7ebf, \u692d\u5706, \u53cc\u66f2\u7ebf\u7684\u7279\u5f81\u4e0e\u56fe\u5f62<\/h1>\n<p><em><strong>\u6458\u8981:<\/strong><br \/>\n\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u590d\u4e60\u5706\u9525\u66f2\u7ebf\uff08\u629b\u7269\u7ebf\u3001\u692d\u5706\u548c\u53cc\u66f2\u7ebf\uff09\uff0c\u4ece\u5b83\u4eec\u7684\u6807\u51c6\u65b9\u7a0b\u548c\u901a\u7528\u65b9\u7a0b\u5f00\u59cb\u3002\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u8bc6\u522b\u548c\u63cf\u8ff0\u6bcf\u6761\u66f2\u7ebf\uff0c\u91cd\u70b9\u5173\u6ce8\u629b\u7269\u7ebf\u7684\u9876\u70b9\u3001\u7126\u70b9\u548c\u5bf9\u79f0\u8f74\u7b49\u5173\u952e\u8981\u7d20\uff0c\u4ee5\u53ca\u901a\u8fc7\u7cfb\u6570\u7b26\u53f7\u533a\u5206\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u3002<br \/>\n<\/em><br \/>\n<strong>\u5b66\u4e60\u76ee\u6807:<\/strong><br \/>\n\u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u8bc6\u522b<\/strong>\u5706\u9525\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\uff08\u629b\u7269\u7ebf\u3001\u692d\u5706\u3001\u53cc\u66f2\u7ebf\uff09<\/li>\n<li><strong>\u8ba1\u7b97<\/strong>\u5706\u9525\u66f2\u7ebf\u7684\u5404\u4e2a\u7279\u5f81\uff1a\u534a\u8f74\u957f\u5ea6\u3001\u7126\u8ddd\u3001\u51c6\u7ebf\u7b49\u3002<\/li>\n<\/ol>\n<p><strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n<a href=\"#1\">\u5706\u9525\u66f2\u7ebf<\/a><br \/>\n<a href=\"#2\">\u629b\u7269\u7ebf\u590d\u4e60<\/a><br \/>\n<a href=\"#3\">\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u590d\u4e60<\/a><br \/>\n<a href=\"#4\">\u692d\u5706\u7684\u7279\u5f81<\/a><br \/>\n<a href=\"#5\">\u53cc\u66f2\u7ebf\u7684\u7279\u5f81<\/a><br \/>\n<a href=\"#6\">\u89e3\u7b54\u7ec3\u4e60<\/a>\n<\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/d21_9EHUv_M\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u5706\u9525\u66f2\u7ebf<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=d21_9EHUv_M&amp;t=126s\" target=\"_blank\" rel=\"noopener\"><strong>\u5706\u9525\u66f2\u7ebf\u662f\u6307<\/strong><\/a>\u5706\u9525\u8868\u9762\u4e0e\u5e73\u9762\u76f8\u4ea4\u4ea7\u751f\u7684\u6240\u6709\u66f2\u7ebf\u3002\u5706\u9525\u66f2\u7ebf\u5bb6\u65cf\u5305\u62ec\u5706\u548c\u692d\u5706\uff0c\u4ee5\u53ca\u53cc\u66f2\u7ebf\uff0c\u8fd9\u4e9b\u66f2\u7ebf\u6211\u4eec\u5df2\u7ecf\u5b66\u4e60\u8fc7\u4e86\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-5eckvpNxzlg\/YJJimcxkMYI\/AAAAAAAAFEA\/dfGTvXblcD4dZXSjpWvonYFN8O0EMNqtwCLcBGAsYHQ\/s0\/curvas-conicas-secciones-cono.png\" alt=\"\u5706\u9525\u66f2\u7ebf\" class=\" aligncenter lazyload\" width=\"531\" height=\"272\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-5eckvpNxzlg\/YJJimcxkMYI\/AAAAAAAAFEA\/dfGTvXblcD4dZXSjpWvonYFN8O0EMNqtwCLcBGAsYHQ\/s0\/curvas-conicas-secciones-cono.png\" alt=\"\u5706\u9525\u66f2\u7ebf\" class=\" aligncenter lazyload\" width=\"531\" height=\"272\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u73b0\u5728\u6211\u4eec\u5c06\u590d\u4e60\u5982\u4f55\u8bc6\u522b\u548c\u63cf\u8ff0\u8fd9\u4e9b\u66f2\u7ebf\u3002\u6211\u4eec\u5c06\u7279\u522b\u5173\u6ce8\u6807\u51c6\u5f62\u5f0f\uff0c\u56e0\u4e3a\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u5f62\u5f0f\uff0c\u5e76\u4e14\u5728\u8868\u8fbe\u4e0a\u900f\u9732\u7684\u4fe1\u606f\u6700\u5c11\u3002\u76f8\u53cd\uff0c\u901a\u7528\u65b9\u7a0b\u51e0\u4e4e\u63ed\u793a\u4e86\u6240\u6709\u51e0\u4f55\u7279\u5f81\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u629b\u7269\u7ebf\u590d\u4e60<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=d21_9EHUv_M&amp;t=160s\" target=\"_blank\" rel=\"noopener\"><strong>\u6bcf\u6761\u629b\u7269\u7ebf\u7684\u8868\u793a<\/strong><\/a>\u65b9\u7a0b\u5f62\u5f0f\u5982\u4e0b<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y=ax^2 + bx + c,<\/span> \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>\n<p style=\"text-align: justify;\">\u6839\u636e\u8fd9\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u5f97\u5230\u4e86:<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u9876\u70b9\u5750\u6807: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle (x_0, y_0)=\\left( -\\dfrac{b}{2a}, c - \\dfrac{b^2}{4a} \\right)<\/span><\/li>\n<li>\u7126\u8ddd: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f=\\dfrac{1}{4a}<\/span><\/li>\n<li>\u7126\u70b9\u5750\u6807: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle foco=\\left( -\\dfrac{b}{2a}, c - \\dfrac{b^2}{4a} + f \\right) =\\left( -\\dfrac{b}{2a}, c + \\dfrac{1- b^2}{4a} \\right)<\/span><\/li>\n<li>\u51c6\u7ebf\u65b9\u7a0b: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle y= c - \\dfrac{b^2}{4a} - f = c - \\dfrac{1+b^2}{4a}<\/span><\/li>\n<li>\u5bf9\u79f0\u8f74\u65b9\u7a0b: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle x= -\\dfrac{b}{2a} <\/span><\/li>\n<li>\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff08\u5982\u679c\u5b58\u5728\uff09: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle x_{1,2}= \\dfrac{-b \\pm \\sqrt{b^2-4ac}}{2a} <\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed8\u5236\u51fa\u4efb\u4f55\u629b\u7269\u7ebf\u7684\u56fe\u5f62\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u590d\u4e60<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=d21_9EHUv_M&amp;t=449s\" target=\"_blank\" rel=\"noopener\"><strong>\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u8868\u8fbe\u5f0f\u4e3a<\/strong><\/a>:<\/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;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u662f\u975e\u96f6\u5e38\u6570\uff0c\u6839\u636e\u6211\u4eec\u5b66\u5230\u7684\u5185\u5bb9\uff0c\u7ed3\u8bba\u5982\u4e0b:<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u7b26\u53f7\u76f8\u540c\uff0c\u5219\u4e3a\u692d\u5706\u3002<\/li>\n<li>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u7b26\u53f7\u76f8\u53cd\uff0c\u5219\u4e3a\u53cc\u66f2\u7ebf\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u4e3a\u4e86\u6e05\u695a\u5730\u533a\u5206\u8fd9\u4e24\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u6210:<\/p>\n<ul style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha x^2+ \\beta x + \\gamma y^2 + \\delta y + \\epsilon = 0<\/span> \u4e3a\u692d\u5706\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha x^2+ \\beta x - \\gamma y^2 + \\delta y + \\epsilon = 0<\/span> \u4e3a\u53cc\u66f2\u7ebf\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\beta, \\gamma, \\delta<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span> \u662f\u4efb\u610f\u5b9e\u6570\uff0c\u4e14 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span> \u6c38\u8fdc\u4e3a\u6b63\u3002\u8fd9\u6837\u5199\u53ef\u4ee5\u6e05\u695a\u5730\u533a\u5206\u4e24\u79cd\u60c5\u51b5\u3002\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad\u51fa\u4ee5\u4e0b\u7ed3\u8bba:<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u692d\u5706\u7684\u7279\u5f81<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=d21_9EHUv_M&amp;t=552s\" target=\"_blank\" rel=\"noopener\"><strong>\u4ece\u6807\u51c6\u65b9\u7a0b\u5f00\u59cb\uff0c<\/strong><\/a> \u6211\u4eec\u5f97\u51fa\u4ee5\u4e0b\u63a8\u8bba:<\/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\">\\alpha x^2+ \\beta x + \\gamma y^2 + \\delta y + \\epsilon = 0<\/span><\/td>\n<td>; \u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\u3002<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\left( x^2+ \\dfrac{\\beta}{\\alpha }x\\right) + \\gamma \\left(y^2 + \\dfrac{\\delta}{\\gamma }y\\right) =- \\epsilon<\/span><\/td>\n<td>; \u56e0\u5f0f\u5206\u89e3\u5e76\u91cd\u65b0\u5206\u7ec4<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2 + \\gamma \\left(y + \\dfrac{\\delta}{2 \\gamma } \\right)^2 =\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon<\/span><\/td>\n<td>; \u5b8c\u6210\u5e73\u65b9\u5e76\u91cd\u65b0\u5206\u7ec4<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\dfrac{\\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2}{\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} + \\gamma \\dfrac{\\left(y + \\dfrac{\\delta}{2 \\gamma } \\right)^2}{\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} = 1<\/span><\/td>\n<td>; \u5c06\u6240\u6709\u9879\u9664\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon<\/span><\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2}{\\dfrac{1}{\\alpha }\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} + \\dfrac{\\left(y + \\dfrac{\\delta}{2 \\gamma } \\right)^2}{\\dfrac{1}{ \\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} = 1<\/span><\/td>\n<td>; \u91cd\u7ec4 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left( \\dfrac{ x - \\left(-\\dfrac{\\beta}{2 \\alpha }\\right)}{\\sqrt{\\dfrac{1}{\\alpha}\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}}\\right)^2 + \\left( \\dfrac{y - \\left(-\\dfrac{\\delta}{2 \\gamma } \\right)}{\\sqrt{\\dfrac{1}{\\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}}\\right)^2 = 1<\/span><\/td>\n<td>; \u4f7f\u7528\u5e73\u65b9\u6839\u8fdb\u884c\u91cd\u7ec4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u5728\u8fd9\u4e2a\u63a8\u8bba\u7684\u7b2c (3) \u6b65\u4e2d\u5c24\u4e3a\u91cd\u8981\u7684\u662f\uff0c\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon<\/span> \u7684\u503c\u4e3a\u8d1f\u6570\uff0c\u90a3\u4e48\u692d\u5706\u5c06\u4e0d\u5b58\u5728\u3002<\/p>\n<p style=\"text-align: justify;\">\u8bf7\u8bb0\u4f4f\uff0c\u692d\u5706\u7684\u901a\u7528\u65b9\u7a0b\u5f62\u5f0f\u4e3a:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left( \\dfrac{x-h}{a} \\right)^2 + \\left(\\dfrac{y-k}{b} \\right)^2 = 1<\/span>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e2a\u7ed3\u679c\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4ece\u901a\u7528\u65b9\u7a0b\u4e2d\u83b7\u5f97\u6240\u6709\u9690\u85cf\u7684\u4fe1\u606f:<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u4e2d\u5fc3\u5750\u6807: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle (h,k) = \\left( -\\dfrac{\\beta}{2\\alpha}, -\\dfrac{\\delta}{2\\gamma}\\right)<\/span><\/li>\n<li>\u6c34\u5e73\u534a\u8f74\u957f\u5ea6: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle a = \\sqrt{\\dfrac{1}{\\alpha}\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}<\/span><\/li>\n<li>\u5782\u76f4\u534a\u8f74\u957f\u5ea6: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle b = \\sqrt{\\dfrac{1}{\\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } + \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u6709\u4e86\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u76f4\u63a5\u4ece\u6807\u51c6\u65b9\u7a0b\u7ed8\u5236\u692d\u5706\u7684\u56fe\u5f62\u3002\u5176\u56fe\u5f62\u5982\u4e0b\u6240\u793a:<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-aVD7YQ7DfL0\/YJKBv9QXeTI\/AAAAAAAAFEQ\/urCuFtrn-YYBQ_fVSGXsmhMqExFumag-ACLcBGAsYHQ\/s0\/elipse.PNG\" class=\" aligncenter lazyload\" width=\"414\" height=\"291\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-aVD7YQ7DfL0\/YJKBv9QXeTI\/AAAAAAAAFEQ\/urCuFtrn-YYBQ_fVSGXsmhMqExFumag-ACLcBGAsYHQ\/s0\/elipse.PNG\" class=\" aligncenter lazyload\" width=\"414\" height=\"291\" \/><\/noscript><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u53cc\u66f2\u7ebf\u7684\u7279\u5f81<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=d21_9EHUv_M&amp;t=911s\" target=\"_blank\" rel=\"noopener\"><strong>\u901a\u8fc7\u5b8c\u5168\u7c7b\u4f3c\u7684\u63a8\u7406\u65b9\u6cd5\uff0c<\/strong><\/a> \u4f60\u53ef\u4ee5\u4ece\u6807\u51c6\u65b9\u7a0b\u51fa\u53d1\uff0c\u5b8c\u6210\u5bf9\u53cc\u66f2\u7ebf\u7684\u5168\u9762\u63cf\u8ff0\u3002\u5b9e\u9645\u4e0a\uff0c\u5206\u6790\u5982\u6b64\u76f8\u4f3c\uff0c\u4ee5\u81f3\u4e8e\u6211\u53ef\u4ee5\u590d\u5236\u692d\u5706\u7684\u5206\u6790\uff0c\u53ea\u9700\u8981\u66f4\u6539\u4e00\u4e9b\u90e8\u5206\u3002<\/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\">\\alpha x^2+ \\beta x - \\gamma y^2 + \\delta y + \\epsilon = 0<\/span><\/td>\n<td>; \u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u3002<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\left( x^2+ \\dfrac{\\beta}{\\alpha }x\\right) - \\gamma \\left(y^2 - \\dfrac{\\delta}{\\gamma }y\\right) =- \\epsilon<\/span><\/td>\n<td>; \u56e0\u5f0f\u5206\u89e3\u5e76\u91cd\u65b0\u5206\u7ec4<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2 - \\gamma \\left(y - \\dfrac{\\delta}{2 \\gamma } \\right)^2 =\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon<\/span><\/td>\n<td>; \u5b8c\u6210\u5e73\u65b9\u5e76\u91cd\u65b0\u5206\u7ec4<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\alpha \\dfrac{\\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2}{\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} - \\gamma \\dfrac{\\left(y - \\dfrac{\\delta}{2 \\gamma } \\right)^2}{\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} = 1<\/span><\/td>\n<td>; \u5c06\u6240\u6709\u9879\u9664\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon<\/span><\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{\\left( x + \\dfrac{\\beta}{2 \\alpha }\\right)^2}{\\dfrac{1}{\\alpha}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} - \\dfrac{\\left(y - \\dfrac{\\delta}{2 \\gamma } \\right)^2}{\\dfrac{1}{\\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)} = 1<\/span><\/td>\n<td>; \u91cd\u7ec4 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left( \\dfrac{ x - \\left(-\\dfrac{\\beta}{2 \\alpha }\\right)}{\\sqrt{\\dfrac{1}{\\alpha}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}}\\right)^2 - \\left( \\dfrac{y - \\left(\\dfrac{\\delta}{2 \\gamma } \\right)}{\\sqrt{\\dfrac{1}{\\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}}\\right)^2 = 1<\/span><\/td>\n<td>; \u4f7f\u7528\u5e73\u65b9\u6839\u8fdb\u884c\u91cd\u7ec4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e9b\u63a8\u8bba\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u8fc5\u901f\u7ed8\u5236\u51fa\u53cc\u66f2\u7ebf\u7684\u56fe\u5f62\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\dfrac{x-h}{a} \\right)^2 - \\left(\\dfrac{y-k}{b} \\right)^2 =1 <\/span>\n<p style=\"text-align: justify;\">\u4e0e\u692d\u5706\u4e0d\u540c\u7684\u662f\uff0c\u8fd9\u91cc\u66f4\u9002\u5408\u4f7f\u7528\u201c\u751f\u6210\u6846\u201d\u7684\u8bf4\u6cd5\uff0c\u89c1\u4e0b\u56fe\u6240\u793a:<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u4e2d\u5fc3\u5750\u6807: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle (h,k) = \\left( -\\dfrac{\\beta}{2\\alpha}, \\dfrac{\\delta}{2\\gamma}\\right)<\/span><\/li>\n<li>\u6c34\u5e73\u534a\u8f74\u957f\u5ea6: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle a = \\sqrt{\\dfrac{1}{\\alpha}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}<\/span><\/li>\n<li>\u5782\u76f4\u534a\u8f74\u957f\u5ea6: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle b = \\sqrt{\\dfrac{1}{\\gamma}\\left(\\dfrac{\\beta^2}{4\\alpha } - \\dfrac{\\delta^2}{4\\gamma } - \\epsilon\\right)}<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-bd0n_BuEFiE\/YJKJ1fPDhMI\/AAAAAAAAFEY\/-QjR2QbycSkKJihjHnwmdIDESYgNDyuBgCLcBGAsYHQ\/s0\/hiperbola.PNG\" alt=\"\u53cc\u66f2\u7ebf\" class=\" aligncenter lazyload\" width=\"428\" height=\"305\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-bd0n_BuEFiE\/YJKJ1fPDhMI\/AAAAAAAAFEY\/-QjR2QbycSkKJihjHnwmdIDESYgNDyuBgCLcBGAsYHQ\/s0\/hiperbola.PNG\" alt=\"\u53cc\u66f2\u7ebf\" class=\" aligncenter lazyload\" width=\"428\" height=\"305\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e9b\u5206\u6790\u7ed3\u679c\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u7ed8\u5236\u51fa\u5706\u9525\u66f2\u7ebf\u65cf\u4e2d\u7684\u4efb\u4f55\u6210\u5458\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u89e3\u7b54\u7ec3\u4e60<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PKjQrcC0HG4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5706\u9525\u66f2\u7ebf: \u629b\u7269\u7ebf, \u692d\u5706, \u53cc\u66f2\u7ebf\u7684\u7279\u5f81\u4e0e\u56fe\u5f62 \u6458\u8981: \u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u590d\u4e60\u5706\u9525\u66f2\u7ebf\uff08\u629b\u7269\u7ebf\u3001\u692d\u5706\u548c\u53cc\u66f2\u7ebf\uff09\uff0c\u4ece\u5b83\u4eec\u7684\u6807\u51c6\u65b9\u7a0b\u548c\u901a\u7528\u65b9\u7a0b\u5f00\u59cb\u3002\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u8bc6\u522b\u548c\u63cf\u8ff0\u6bcf\u6761\u66f2\u7ebf\uff0c\u91cd\u70b9\u5173\u6ce8\u629b\u7269\u7ebf\u7684\u9876\u70b9\u3001\u7126\u70b9\u548c\u5bf9\u79f0\u8f74\u7b49\u5173\u952e\u8981\u7d20\uff0c\u4ee5\u53ca\u901a\u8fc7\u7cfb\u6570\u7b26\u53f7\u533a\u5206\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u3002 \u5b66\u4e60\u76ee\u6807: \u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f: \u8bc6\u522b\u5706\u9525\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\uff08\u629b\u7269\u7ebf\u3001\u692d\u5706\u3001\u53cc\u66f2\u7ebf\uff09 \u8ba1\u7b97\u5706\u9525\u66f2\u7ebf\u7684\u5404\u4e2a\u7279\u5f81\uff1a\u534a\u8f74\u957f\u5ea6\u3001\u7126\u8ddd\u3001\u51c6\u7ebf\u7b49\u3002 \u5185\u5bb9\u7d22\u5f15 \u5706\u9525\u66f2\u7ebf \u629b\u7269\u7ebf\u590d\u4e60 \u692d\u5706\u548c\u53cc\u66f2\u7ebf\u590d\u4e60 \u692d\u5706\u7684\u7279\u5f81 \u53cc\u66f2\u7ebf\u7684\u7279\u5f81 \u89e3\u7b54\u7ec3\u4e60 \u5706\u9525\u66f2\u7ebf \u5706\u9525\u66f2\u7ebf\u662f\u6307\u5706\u9525\u8868\u9762\u4e0e\u5e73\u9762\u76f8\u4ea4\u4ea7\u751f\u7684\u6240\u6709\u66f2\u7ebf\u3002\u5706\u9525\u66f2\u7ebf\u5bb6\u65cf\u5305\u62ec\u5706\u548c\u692d\u5706\uff0c\u4ee5\u53ca\u53cc\u66f2\u7ebf\uff0c\u8fd9\u4e9b\u66f2\u7ebf\u6211\u4eec\u5df2\u7ecf\u5b66\u4e60\u8fc7\u4e86\u3002 \u73b0\u5728\u6211\u4eec\u5c06\u590d\u4e60\u5982\u4f55\u8bc6\u522b\u548c\u63cf\u8ff0\u8fd9\u4e9b\u66f2\u7ebf\u3002\u6211\u4eec\u5c06\u7279\u522b\u5173\u6ce8\u6807\u51c6\u5f62\u5f0f\uff0c\u56e0\u4e3a\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u5f62\u5f0f\uff0c\u5e76\u4e14\u5728\u8868\u8fbe\u4e0a\u900f\u9732\u7684\u4fe1\u606f\u6700\u5c11\u3002\u76f8\u53cd\uff0c\u901a\u7528\u65b9\u7a0b\u51e0\u4e4e\u63ed\u793a\u4e86\u6240\u6709\u51e0\u4f55\u7279\u5f81\u3002 \u629b\u7269\u7ebf\u590d\u4e60 \u6bcf\u6761\u629b\u7269\u7ebf\u7684\u8868\u793a\u65b9\u7a0b\u5f62\u5f0f\u5982\u4e0b \u5176\u4e2d \u6839\u636e\u8fd9\u4e2a\u65b9\u7a0b\uff0c\u6211\u4eec\u5f97\u5230\u4e86: \u9876\u70b9\u5750\u6807: \u7126\u8ddd: \u7126\u70b9\u5750\u6807: \u51c6\u7ebf\u65b9\u7a0b: \u5bf9\u79f0\u8f74\u65b9\u7a0b: \u4e0ex\u8f74\u7684\u4ea4\u70b9\uff08\u5982\u679c\u5b58\u5728\uff09: \u901a\u8fc7\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed8\u5236\u51fa\u4efb\u4f55\u629b\u7269\u7ebf\u7684\u56fe\u5f62\u3002 \u692d\u5706\u548c\u53cc\u66f2\u7ebf\u590d\u4e60 \u692d\u5706\u548c\u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u8868\u8fbe\u5f0f\u4e3a: \u5176\u4e2d \u548c \u662f\u975e\u96f6\u5e38\u6570\uff0c\u6839\u636e\u6211\u4eec\u5b66\u5230\u7684\u5185\u5bb9\uff0c\u7ed3\u8bba\u5982\u4e0b: \u5982\u679c \u548c \u7b26\u53f7\u76f8\u540c\uff0c\u5219\u4e3a\u692d\u5706\u3002 \u5982\u679c \u548c \u7b26\u53f7\u76f8\u53cd\uff0c\u5219\u4e3a\u53cc\u66f2\u7ebf\u3002 \u4e3a\u4e86\u6e05\u695a\u5730\u533a\u5206\u8fd9\u4e24\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u6210: \u4e3a\u692d\u5706\u3002 \u4e3a\u53cc\u66f2\u7ebf\u3002 \u5176\u4e2d \u548c \u662f\u4efb\u610f\u5b9e\u6570\uff0c\u4e14 \u548c \u6c38\u8fdc\u4e3a\u6b63\u3002\u8fd9\u6837\u5199\u53ef\u4ee5\u6e05\u695a\u5730\u533a\u5206\u4e24\u79cd\u60c5\u51b5\u3002\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad\u51fa\u4ee5\u4e0b\u7ed3\u8bba: \u692d\u5706\u7684\u7279\u5f81 \u4ece\u6807\u51c6\u65b9\u7a0b\u5f00\u59cb\uff0c \u6211\u4eec\u5f97\u51fa\u4ee5\u4e0b\u63a8\u8bba: (1) ; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29020,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":40,"footnotes":""},"categories":[591,575],"tags":[],"class_list":["post-29025","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>\u5706\u9525\u66f2\u7ebf: \u629b\u7269\u7ebf, \u692d\u5706, \u53cc\u66f2\u7ebf\u7684\u7279\u5f81\u4e0e\u56fe\u5f62 - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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