题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-22289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-64570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-47651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-48901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-47487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-30268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-48976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-80682.png)
(1)求椭圆的方程;
(2)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
(3)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-30753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-55184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-30544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-34454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-38156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-67767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-68421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-39824.png)
解析
试题分析:(1)根据椭圆的几何性质求出椭圆标准方程中的
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-66101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-47430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-34454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-84723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-38156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-67767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-38156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
试题解析:(1)由题意可得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-38007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-73385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-88159.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231041-53919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-68421.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231041-75125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231041-91968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231041-99015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231042-65992.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231042-52521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231042-21304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-39824.png)
即动点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231037-59532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-61395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-39824.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231042-30563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-34454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231042-90172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231040-47430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231043-60205.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231043-68050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231043-20440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231043-19738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231043-17027.png)
∴点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231038-34454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231044-91123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-38156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231044-71133.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231044-37780.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231044-46307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231045-91678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231045-62235.png)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231045-74464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231045-59446.png)
∴圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231046-83441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231046-42885.png)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231039-31205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231046-83441.png)
核心考点
试题【设椭圆的左右顶点分别为,离心率.过该椭圆上任一点作轴,垂足为,点在的延长线上,且.(1)求椭圆的方程;(2)求动点的轨迹的方程;(3)设直线(点不同于)与直线交】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231025-11897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231026-79891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231026-23882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231027-45275.png)
(1)求曲线C的直角坐标方程;
(2)设直线l与曲线C相交于A、B两点,当a变化时,求|AB|的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-89497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-13653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-89497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-15201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231016-13653.png)
(1)求曲线C的方程;
(2)若过点M
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-84309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-21563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-10180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231017-13318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231018-68940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231004-84408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231004-78775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-85644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-15960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-72225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-23905.png)
(1)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231005-72225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-70441.png)
(2)若过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-37336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-79790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-70441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231006-46887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231007-71387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025231007-11365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230952-50555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230952-98389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230952-88310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230952-21637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230952-26899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-63728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-16849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-54197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-67213.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230954-18584.png)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-54197.png)
(3)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230953-63728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025230954-46115.png)
A.y=![]() | B.y=-![]() | C.x=![]() | D.x=- ![]() |
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