题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141040-94439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141040-95938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141040-33147.png)
(1)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141040-29098.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-84211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-25826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-98239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141042-98802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141042-19530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141042-66310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141040-29098.png)
(3)在(2)的条件下,设点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141042-70830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-63543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-94306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141042-70830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-30661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-94306.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-97061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-94306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-81855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-69832.png)
解析
试题分析:(1)求动点轨迹方程,分四步.第一步,设动点坐标
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-40704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-33581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-83390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-10877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-97938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-52145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-76009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-42652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-27756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-97061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-64959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-22483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-18275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-58174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-16923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-14214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-81321.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-36021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-88425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-78699.png)
解析:(1) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141049-51848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-33581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141049-86665.png)
所以,点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141049-77501.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-10877.png)
椭圆的方程
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-97938.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141041-97377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141045-52145.png)
将①代入②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141049-61378.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-52976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-48332.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-24921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-42652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-27756.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-97061.png)
(3) 假设存在椭圆上的一点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141046-64959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-47282.png)
则Q到直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-47282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141050-68994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-22483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-18275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-58174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141047-16923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141051-21983.png)
化简整理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-81321.png)
∵ 点在椭圆上,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-36021.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-88425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141048-78699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141051-29138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141051-38827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141051-52688.png)
∴ 椭圆上存在点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141043-94306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-81855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141044-69832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141052-52720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141052-22217.png)
核心考点
试题【已知,点依次满足。(1)求点的轨迹; (2)过点作直线交以为焦点的椭圆于两点,线段的中点到轴的距离为,且直线与点的轨迹相切,求该椭圆的方程;(3)在(2)的条】;主要考察你对直线方程的几种形式等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141018-86118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141018-51018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141018-75973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141018-95030.png)
(1)求椭圆的方程;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-85305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-35411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-84578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-11230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-68481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-73450.png)
(3)在(2)的条件下,试问
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141019-57712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-30507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-28777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-53419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-62796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-28777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022141020-77294.png)
A.经过定点![]() ![]() |
B.经过定点![]() ![]() |
C.经过任意两个不同的点![]() ![]() ![]() |
D.不经过原点的直线都可以用方程![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140947-37539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140947-34762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140947-37539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140942-20294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140942-76877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140943-78438.png)
A.4 | B.2 | C.1 | D.3 |
(1)求抛物线C的方程,并求其准线方程;
(2)是否存在平行于OA(O为坐标原点)的直线l,使得直线l与抛物线C有公共点,且直线OA与l的距离等于
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022140934-89325.png)
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