圆锥曲线方程椭圆-课件【PPT讲稿】.ppt

一、知识梳理时动点不存在。当动点的轨迹为线段= 当动点的轨迹为椭圆当等于常数的距离的和, 平面内与两个定点定义||2 FF ||2 ||2 2 FF 121 21 21 21 21FFa FFa FFa a?????????? cFFcFc xbab ya x2||0,,0,F 011 2 21 2 1 2 22 2??????焦距焦点轴上, 焦点在式椭圆的标准方程两种形???????? cFFcFc ybab xa y2||,0,,0F 012 21 2 1 2 22 2??????焦距焦点轴上, 焦点在 222cba??这里叫做焦点定直线叫做准线,定点叫做离心率, 则轨迹是椭圆若等于常数的距离之比和到定直线点第二定义,平面内到定 e ee lF,,10, 3??离心率准线焦距焦点对称轴范围顶点图形标准方程?? 01 2 22 2????bab ya x?? 01 2 22 2????bab xa yF 1F 2M ???????? bBbBaAaA,0,.0,0,,0, 2121?????????? aBaBbAbA,0,.0,0,,0, 2121??byax??, aybx??, 222 1)0,( ),0,(bac cFcF??? 222 1),0( ),,0(bac cFcF???cFF2|| 21?cFF2|| 21? c ax 2??c ay 2??10???ea ce 坐标轴坐标轴通径离心率准线焦距焦点坐标轴坐标轴对称轴范围顶点图形标准方程 222 21)0,( ),0,(bac cFcF??? 222 21),0( ),,0(bac cFcF???cFF2|| 21?cFF2|| 21? c ax 2??c ay 2??10???ea ce??焦半径 0,0yxMa b AB 22||? 02 01|| || exa MF exa MF ???? 02 01|| || eya MF eya MF ????的横坐标的取值范围是为钝角时,点为其上的动点,当,点的焦点为+ 椭圆例P PF F PFF yx 21 21 22149 : ??52,3 50505 21 2 1???FFa ceF F ), , ( ) , (- 解: 04 0 2 )2( cos 2 22 21 21 2 22 2121????????c PF PF PF PF c PF PF PF F5 35 3 0 0 2 0 1??????x ex a PF ex a PF - 代入解得???1 .4 2 22 2b ya x 椭圆参数方程: ??????? sin cos by ax??长轴时称为,当焦点弦垂直于椭圆,焦点到相应准线距离,最长距离距离短它的焦点与椭圆上的最椭圆, 2 22 2????bab ya xca?ca? c b 2 通径其长为为焦准距) Pa bp( 22 2?????称为焦点三角形。构成的与两焦点上一点椭圆 21 00 2 22 2, PF F yxPbab ya x?????1 2 cos , 21 2 21???? PF PF b PF F= 则若??最大, 为短轴端点时, 时当? P PF PF 21?bc S by yc PF PF S PF F PF F 的最大值为即为短轴端点时, 当 21 21, sin 2 1 0 0 21??????? PF 1F 2?的个数为点的上满足的焦点,在: 是椭圆例P PF PF C yxCFF 21 22 21148 . ???个点,共四象限中各有一个解: 4 60 3 tanP b c????????的范围。,求= ,使如果椭圆上存在一点是椭圆左右焦点和变式:已知椭圆 e QF FQ FFbab ya x??????120 , ),0(1 21 21 2 22 2BF 1F 2?