![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/images0.png)
如图,A为椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/0.png)
=1(a>b>0)上的一个动点,弦AB、AC分别过焦点F
1、F
2,当AC垂直于x轴时,恰好有AF
1:AF
2=3:1.
(Ⅰ)求椭圆的离心率;
(Ⅱ)设
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/1.png)
=λ
1![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/2.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/3.png)
=λ
2![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224709129870416/SYS201311012247091298704019_ST/4.png)
.
①当A点恰为椭圆短轴的一个端点时,求λ
1+λ
2的值;
②当A点为该椭圆上的一个动点时,试判断是λ
1+λ
2否为定值?若是,请证明;若不是,请说明理由.
考点分析:
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