设A(x
1,y
1),B(x
2,y
2)是椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/0.png)
,(a>b>0)上的两点,已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/1.png)
=(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/2.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/3.png)
),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/4.png)
=(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/5.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/6.png)
),且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/7.png)
,若椭圆的离心率
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707021_ST/8.png)
,短轴长为2,O为坐标原点:
(Ⅰ)求椭圆的方程;
(Ⅱ)若直线AB过椭圆的焦点F(0,c),(c为半焦距),求直线AB的斜率k的值;
(Ⅲ)试问:△AOB的面积是否为定值?如果是,请给予证明;如果不是,请说明理由.
考点分析:
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