1 . 已知椭圆
的左,右焦点
、
.若以椭圆的焦点为顶点,以椭圆长轴的顶点为焦点作一双曲线恰为等轴双曲线.
(1)求椭圆的离心率;
(2)设L为过椭圆右焦点
的直线,交椭圆于
、
两点,当
周长为
时;求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9792472d1487fd51ca8d8aff28c151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求椭圆的离心率;
(2)设L为过椭圆右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985b383be47791e0409e542225982299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985b383be47791e0409e542225982299.png)
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2 . 有一凸透镜其剖面图(如图)是由椭圆
和双曲线
的实线部分组成,已知两曲线有共同焦点M、N;A、B分别在左右两部分实线上运动,则
周长的最小值为:
![](https://img.xkw.com/dksih/QBM/2017/4/19/1668989218242560/1669072982794240/STEM/779fed06b9e94b65a9d1e255f9f6a77d.png?resizew=208)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392d61933568d27a27568c6298365bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c128084a819612b0367450f0961238b0.png)
![](https://img.xkw.com/dksih/QBM/2017/4/19/1668989218242560/1669072982794240/STEM/705ebfe6e3bd49fca461e0e54ad4a97a.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2017/4/19/1668989218242560/1669072982794240/STEM/779fed06b9e94b65a9d1e255f9f6a77d.png?resizew=208)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2017-04-19更新
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4944次组卷
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4卷引用:2016-2017学年湖北省襄阳市四校(襄州一中、枣阳一中、宜城一中、曾都一中)高二下学期期中联考数学(文)试卷