1如图，内外两个椭圆的离心率相同，从外层椭圆顶点向内层椭圆引切线AC，BD，设内层椭圆方程为http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_ST.files/image002.png ，则椭圆的离心率为（   ）

http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_ST.files/image003.jpg

A. http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_ST.files/image007.png 

答案：C

试题分析：如果两个椭圆的离心率相等，那么就称这两个椭圆相似

设外层椭圆方程为http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_DA.files/image008.png.

由http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_DA.files/image016.png.

所以http://img.manfen5.com/res/gzsx/web/STSource/2013122509351724113914/SYS201312250935510397758994_DA.files/image021.png,故选C.

考点：椭圆的简单性质和直线与椭圆的位置关系.

2 若两个椭圆的离心率相等,我们称这两个椭圆相似,已知椭圆x^2/4+y^2/m=1与椭圆x^2/m+y^2/9=1相似，则m的值为 A.8 B.6 C.4 D.3

答案：B

4:m=m:9   ;    m^2=36  , m=6