题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235604-76678.png)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-32921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-25988.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-11935.png)
解析
试题分析:(Ⅰ)设椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-67992.png)
易知抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235604-76678.png)
根据椭圆的定义
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235606-10093.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235606-93312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235606-29583.png)
所以椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-11935.png)
(II)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235607-85496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235607-41765.png)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235607-59364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235607-11306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235608-50075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235608-27729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235608-50007.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-25988.png)
设(x,y)为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-25988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235609-51007.png)
由斜率为正数,整理得y=2x-1,这就是所求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235605-25988.png)
点评:中档题,求椭圆的标准方程,主要运用了椭圆的几何性质,注意明确焦点轴和a,b,c的关系。曲线关系问题,往往通过联立方程组,得到一元二次方程,运用韦达定理。本题(2)出发利用角的平分线的性质,求得直线方程。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235552-60378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235552-23545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235552-27592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235553-34838.png)
(Ⅰ)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235552-60378.png)
(Ⅱ)设直线与曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235552-60378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235553-60030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235553-83253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235553-80789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235554-20373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235554-50280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235546-48609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235546-75661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235546-45579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235546-45580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235546-41057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235547-71447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235537-78810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235537-91586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235537-18302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-78299.png)
(1)求椭圆C的方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-98270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-36980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-36980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-33694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-65444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-64155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235538-14050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235539-12762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235539-14688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235530-12559.png)
A.![]() | B.(1,0) | C.![]() | D.(0,1) |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235523-61056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235523-72378.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235524-67302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235523-61056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235524-61097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235524-70602.png)
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