题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-10182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-89922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-48377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-89922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151024-67318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-85806.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
(2)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-80436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-15065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-37947.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151026-76310.png)
解析
试题分析:(1)根据椭圆的定义,可判断点的轨迹为椭圆,再根据椭圆的基本量,容易写出椭圆的方程,求曲线的方程一般可设动点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151026-25990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151026-41906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151026-83678.png)
试题解析:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151027-36633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-89922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151022-48377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151027-59025.png)
故曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151023-45547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151026-76310.png)
(2)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151027-82843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151027-15637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151027-36649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151028-98016.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151028-12874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151028-40181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151028-80004.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-80436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151028-16362.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151029-75141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151029-27533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151029-23308.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-15065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151029-99234.png)
即在题设条件下,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151025-37947.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-38005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-91792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-15413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-45559.png)
(1)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151014-62482.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-11929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151015-68172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150959-34916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150959-54151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-92329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-78475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-97956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151000-56364.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-84962.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-94802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-94675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151001-31926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-30235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-84192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151002-56028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023151003-94702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150948-31114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-75697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-88792.png)
(Ⅰ)求动点M的轨迹C的方程;
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-44673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-35463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150949-44678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-89861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-57423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-73073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150936-67086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-20073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-57576.png)
(Ⅰ)求椭圆方程;
(Ⅱ) 直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-42929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-24773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-62441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150937-67414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150925-14348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150926-44085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150926-84762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150926-59884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150926-31104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150927-82127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150927-75196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023150927-48979.jpg)
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