2022年圆锥曲线知识点总结doc资料 .pdf
此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流高中数学圆锥曲线选知识点总结一、椭圆1、定义：平面内与两个定点1F，2F的距离之和等于常数（大于12F F）的点的轨迹称为 椭圆即：|)|2(,2|2121FFaaMFMF。这两个定点称为椭圆的 焦点，两焦点的距离称为椭圆的焦距2、椭圆的几何性质：焦点的位置焦点在x轴上焦点在 y 轴上图形标准方程222210 xyabab222210yxabab范围axa且bybbxb且aya顶点1,0a、2,0a10,b、20,b10,a、20,a1,0b、2,0b轴长短轴的长2b长轴的长2a焦点1,0Fc、2,0Fc10,Fc、20,Fc焦距222122F Fc cab对称性关于x轴、y轴、原点对称离心率22101cbeeaae 越小，椭圆越圆；e 越大，椭圆越扁此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流二、双曲线1、定义：平面内与两个定点1F，2F的距离之差的绝对值等于常数（小于12F F）的点的轨迹称为 双曲线 即：|)|2(,2|2121FFaaMFMF。这两个定点称为 双曲线的焦点，两焦点的距离称为 双曲线的焦距 2、双曲线的几何性质：焦点的位置焦点在x轴上焦点在y轴上图形标准方程222210,0 xyabab222210,0yxabab范围xa 或 xa，yRya或 ya，xR顶点1,0a、2,0a10,a、20,a轴长虚轴的长2b实轴的长2a焦点1,0Fc、2,0Fc10,Fc、20,Fc焦距222122F Fc cab对称性关于x轴、y 轴对称，关于原点中心对称离心率2211cbeeaa，e越大，双曲线的开口越阔渐近线方程byxaayxb5、实轴和虚轴等长的双曲线称为等轴双曲线 三、抛物线文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流1、定义：平面内与一个定点F和一条定直线l的距离相等的点的轨迹称为抛物线定点F称为抛物线的焦点，定直线l称为抛物线的 准线2、抛物线的几何性质：标准方程22ypx0p22ypx0p22xpy0p22xpy0p范围0 x0 x0y0y顶点0,0对称轴x轴y 轴焦点,02pF,02pF0,2pF0,2pF准线方程2px2px2py2py离心率1e，p越大，抛物线的开口越大焦半径0,0()M x y02pMFx02pMFx02pMFy02pMFy通径过抛物线的焦点且垂直于对称轴的弦称为通径：2HHp焦点弦长公式12ABxxp12AByyp3、过抛物线的焦点作垂直于对称轴且交抛物线于、两点的线段，称为抛物线的“通径”，即2p4、关于抛物线焦点弦的几个结论：设AB为过抛物线22(0)ypxp焦点的弦，1122(,)(,)A x yB xy、，直线AB的倾斜角为，则文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流221212,;4px xy yp22;sinpAB 以AB为直径的圆与准线相切；焦点F对AB、在准线上射影的张角为2；112.|FAFBP四、直线与圆锥曲线的位置关系繁琐）利用两点间距离公式（易）利用一般弦长公式（容弦长问题直线与圆锥曲线相交的系）直线与圆锥曲线位置关代数角度（适用于所有)位置关系主要适用于直线与圆的(几何角度关系直线与圆锥曲线的位置直线与圆锥曲线.12.直线与圆锥曲线的位置关系：.从几何角度看：（特别注意）要特别注意当直线与双曲线的渐进线平行时，直线与双曲线只有一个交点；当直线与抛物线的对称轴平行或重合时，直线与抛物线也只有一个交点。.从代数角度看：设直线L 的方程与圆锥曲线的方程联立得到02cbxax。.若a=0，当圆锥曲线是双曲线时，直线L 与双曲线的渐进线平行或重合；当圆锥曲线是抛物线时，直线L 与抛物线的对称轴平行或重合。.若0a，设acb42。a.0时，直线和圆锥曲线相交于不同两点，相交。b.0时，直线和圆锥曲线相切于一点，相切。c.0时，直线和圆锥曲线没有公共点，相离。五、弦长问题：直线与圆锥曲线相交时的弦长问题是一个难点，化解这个难点的方法是：设而不求，根据根与系数的关系，进行整体代入。即当直线k斜率为与圆锥曲线交于点11y,xA，22y,xB时，则AB=2k121xx=2k1212214xxxx文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流=211k21yy=211k212214yyyy文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 ZO3N6N3W3U4文档编码:CV4M9A3X7S4 HL9K9Z3B4E1 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