题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181206-85633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181206-27832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181206-72175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181207-14109.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181207-38460.png)
A.![]() | B.![]() | C.![]() | D.![]() |
答案
解析
分析:将直线方程与椭圆方程联立,得(3+4k2)x2=12.分别过A、B向x轴作垂线,垂足恰为椭圆的两个焦点,说明A,B的横坐标是±1,即方程(3+4k2)x2=12的两个根为±1,代入求出k的值.
解:将直线与椭圆方程联立,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181208-36610.png)
化简整理得(3+4k2)x2=12(*)
因为分别过A、B向x轴作垂线,垂足恰为椭圆的两个焦点,
故方程的两个根为±1.代入方程(*),得k=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181207-57785.png)
故选A.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181157-44385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181158-56446.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181159-90023.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181149-28228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181149-76719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181149-57422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181144-61351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181144-38709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181144-92564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181144-87324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181145-81656.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181145-61563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181145-85941.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181122-56608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181122-64832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181122-60257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181123-44259.gif)
(1) 求椭圆C的方程;
(2) 求线段MN长度的最小值;
(3) 当线段MN的长度最小时,在椭圆C上的T满足:T到直线AS的距离等于
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181123-25413.gif)
试确定点T的个数。
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181106-74804.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181106-17519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181106-44200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181106-17519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181107-88658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181107-75554.gif)
(Ⅰ)求椭圆C的方程;
(II)设过点F不与坐标轴垂直的直线交椭圆C于A、 B两点,线段AB的垂直平分线与
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181107-83499.gif)
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