题目
题型:黑龙江省模拟题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121531-93115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121531-84155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121531-56950.png)
(1)求椭圆C的方程;
(2)若过点M(2,0)的直线与椭圆C相交于两点A,B,设P为椭圆上一点,且满足
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121531-37336.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121531-95168.png)
(2)由题意知直线AB的斜率存在。设AB:y=k(x-2),A(x1,y1),B(x2,y2),P(x,y),
由此可得(1+2k2)x2-8k2x+8k2-2=0
△=64k4-4(2k2+1)(8k2-2)>0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121532-72702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121532-42022.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121532-65419.png)
∴(x1+x2,y1+y2)=t(x,y),
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121532-32122.png)
∵点P在椭圆上,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121533-90096.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121533-40899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121533-77380.png)
∴t2∈(0,4)
∴t∈(-2,0) ∪(0,2)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121513-48145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121513-40227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121513-18165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121513-48818.png)
(1)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121514-63984.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121514-58118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121514-86776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121514-83512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121515-84692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121515-25694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121515-73640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121515-82062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121515-22308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121516-15696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121516-32877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121516-53714.png)
①证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121516-88428.png)
②记△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121517-68782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121517-36287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121517-92460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121517-70437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121517-34397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121518-29847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121518-24055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121450-87546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121451-95494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121451-85142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121451-78384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121451-14120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121451-68150.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121452-43732.png)
(2)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121452-88167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121452-10935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121452-90632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121453-13521.png)
(3)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121453-50455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121453-98500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121453-57248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121454-62838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121454-73837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121454-57985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121454-80013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121454-90390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121455-11557.png)