已知点M在椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100756724435368/SYS201311031007567244353018_ST/0.png)
上,以M为圆心的圆与x轴相切于椭圆的右焦点F.
(1)若圆M与y轴相切,求椭圆的离心率;
(2)若圆M与y轴相交于A,B两点,且△ABM是边长为2的正三角形,求椭圆的方程.
考点分析:
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已知函数
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上的最大值和最小值.
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如图,F
1,F
2分别是双曲线C:
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=1(a,b>0)的左、右焦点,B是虚轴的端点,直线F
1B与C的两条渐近线分别交于P,Q两点,线段PQ的垂直平分线与x轴交与点M,若|MF
2|=|F
1F
2|,则C的离心率是
.
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已知双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100756724435368/SYS201311031007567244353013_ST/0.png)
和椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103100756724435368/SYS201311031007567244353013_ST/1.png)
有相同的焦点,且双曲线的离心率是椭圆离心率的两倍,则双曲线的方程为
.
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