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椭圆的有关性质

2014-03-20 21:20:35| 分类：几何学 | 标签： |举报 |字号大中小订阅

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（1）椭圆上一点与两焦点构成焦点三角形，设两焦点内角分别为A、B，则

tan(A/2)tan(B/2)=(1-e)/(1+e)（e为离心率）

（2）过椭圆外一点P引椭圆的两条切线，其切线夹角平分线同时也平分关于两个焦点的张角。当两切线夹角为直角时，其动点P的轨迹为圆，半径=√(a²+b²)，a、b为长短半轴。

（3）共焦点的两个椭圆，在外椭圆上任意一点引内椭圆的两条切线，两个切点将内椭圆分为两个优劣椭圆弧，其优弧长与两切线长的和为常量。

（4）共焦点的椭圆与双曲线总是垂交的。过椭圆外共焦双曲线上一点引椭圆的两条切线，两个切点将椭圆分为两个优劣椭圆弧，双曲线将劣椭圆弧分为两个亚劣椭圆弧，则两切线长的差=对应两亚劣椭圆弧的差。

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