第十讲圆锥曲线一（椭圆）一【考点提示】（一）定义：1.第一定义：__________________________________________________________________________________________________2.第二定义：__________________________________________________________________________________________________（二）方程：1.标准方程：__________________________________________________________________________________________________2.参数方程：__________________________________________________________________________________________________（三）性质：1.范围：________________________________________________2.离心率：__________________________________________________________________________________________________3.准线：_________________________________________________4.焦半径：____________________________________________________________________________________________________________________________________________________________________________________________________5.通径：_________________________________________________6.焦准距p：_______________________________________________7.切线方程：________________________________________________8.弦长公式：________________________________________________（四）点与椭圆的位置关系：___________________________________________________________________________________________________________________________________________________（五）焦点三角形：1.顶角：_________________________________________________2.焦点三角形面积：_________________________________________3.向量，模长：_____________________________________________________________________________________________（六）常见做法和结论：11.知道求椭圆中的量，椭圆标准方程：_________________________________________________2.椭圆焦点位置不确定，如何设方程：_________________________________________________3.与22221xyab共焦点的椭圆：_________________________________________________4.与22221xyab有相同离心率的椭圆：_________________________________________________5.椭圆中1122FBFB所构成的菱形的内角与椭圆的离心率之间的关系：_________________________________________________6.焦点三角形顶角的范围：_________________________________________________7.椭圆长轴端点为12,AA，是否存在P，使12APA最大，最小？这点位置在哪里？最大，小角如何求？___________________________________________________________________________________________________________________________________________________8.椭圆短轴端点为12,BB，是否存在P，使12BPB最大，最小？这点位置在哪里？最大，小角如何求？___________________________________________________________________________________________________________________________________________________9.直线与椭圆的位置关系？（1）代数方法：_________________________________________________（2）几何方法：_________________________________________________10.直线l交曲线221mxny于,AB两点，,AB中点为M，?lOMkk____________________________________________________________________________________________________________________________________________________________________________________________________二【典例分析】1.椭圆定义的运用2例1平面一动点12,(0,3),(0,3)PFF，且满足129(0)PFPFaaa，则P点轨迹是______________.例2已知椭圆，F1、F2分别为椭圆的左右焦点，点A（1，1）为椭圆内一点，点P为椭圆上一点：求|PA|+|PF1|的最大值和最小值；求|PA|+|PF2|的最小值。例3（2008•浙江）如图，AB是平面a的斜线段，A为斜足，若点P在平面a内运动，...
