题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-89257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-78994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-81640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-45541.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-89257.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-58345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-89257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-11553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-16762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-56186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-74765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-26540.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-30318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-99850.png)
解析
试题分析:(1)首先根据椭圆有一个顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-81640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-45903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-45541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-58998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-86960.png)
(2)分直线的斜率存在与不存在分类讨论,(1)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-78994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-56186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-58345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-73402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-23498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-19164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-27009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-61116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-95979.png)
解:(1)因为椭圆有一个顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-81640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-45903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-45541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-45903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-58998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-86960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-26967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-30318.png)
(2)依题意,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-58345.png)
(1)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214136-78994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-56186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-58345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-73402.png)
(2)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-34437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-23498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214140-19164.png)
由方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214142-52058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-27009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214141-61116.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214142-61753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214142-15317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214137-81640.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214142-74290.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214143-84626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214143-55999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214143-70414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214143-60765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214143-45257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214144-49408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214144-42406.png)
综合(1)、(2)可知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-74765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214138-26540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214139-99850.png)
核心考点
试题【已知椭圆的中心在坐标原点,对称轴为坐标轴,焦点在轴上,有一个顶点为,.(1)求椭圆的方程;(2)过点作直线与椭圆交于两点,线段的中点为,求直线的斜率的取值范围.】;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/20191025/20191025214113-47430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214113-16760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214114-55064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214114-12836.png)
(1)求椭圆C的方程;
(2)是否存在平行于OM的直线l,使得l与椭圆C相交于A、B两点,且以线段AB为直径的圆恰好过原点?若存在,求出直线l的方程;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214105-26545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214106-32475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214106-31001.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214048-18500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-97652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-32565.png)
求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-71819.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-87708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-71819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214050-83692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214050-10336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214050-11298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214050-73889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214051-14868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214049-87708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214051-10707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214051-95196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214051-23667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214052-64865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214051-10707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214052-49499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-61563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-37024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-30073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-66017.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-66017.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-52346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-45073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-52346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214037-66017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-84402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-72554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-52346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-68907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214038-52346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025214039-91067.png)
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