名校
1 . (本题满分14分)
已知椭圆
的右焦点为F,右准线为l,且直线
与
相交于A点.
(Ⅰ)若⊙C经过O、F、A三点,求⊙C的方程;
(Ⅱ)当
变化时, 求证:⊙C经过除原点O外的另一个定点B;
(Ⅲ)若
时,求椭圆离心率e的范围.
已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c5476a69f9ff13691ffe90910e8887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅰ)若⊙C经过O、F、A三点,求⊙C的方程;
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2c82fca3678e76b0cc676e2a7496de.png)
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真题
2 . 设椭圆
的左、右焦点分别为
是椭圆上的一点,
,原点
到直线
的距离为
.
(Ⅰ)证明
;
(Ⅱ)设
为椭圆上的两个动点,
,过原点
作直线
的垂线
,垂足为
,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec56b59d6f2654570c2b5c4fd13a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da0fe4c103f13aaf006b82720d89af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dde0c5e753479ec91f9da7ae3c585c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bd49b0d88f0c0038f1474bb782b69b.png)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4037561c629fd07503c6803e1eb62fb6.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152922a5c9ce0b4e76783c018b40a0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df84f3520397487618cf80f3ea80aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c81d490c018a166d9970b1b5ea0a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2016-11-30更新
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2089次组卷
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2卷引用:2007年普通高等学校招生全国统一考试文科数学卷(天津)