题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-10242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-23157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-67678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-64407.gif)
(1)确定
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-69570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
(2)试判断是否存在这样的
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-69570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-78740.gif)
答案
(1)解法一:设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-91792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-23157.gif)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-34907.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-79532.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182107-59047.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182107-37783.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-67678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182107-77323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182107-87739.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-48779.gif)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-85752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-23570.gif)
解法二:设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182106-79532.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-23386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-67678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-12141.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-67678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-40953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-48779.gif)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-85752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-23570.gif)
(1) 解法一:因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-97845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
(2) 所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-97845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-71656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-68780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-84188.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-28745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-97845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-68078.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-88309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-32766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-89595.gif)
由弦长公式得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-69346.gif)
将直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-23570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182110-18793.gif)
同理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182111-89837.gif)
因为当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-48779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182111-82503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182111-76471.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182111-15663.gif)
假设存在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-48779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-46910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182109-97845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-46042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-46042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182105-25825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-84403.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-38702.gif)
故当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182108-48779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-46910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182112-46042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182113-70950.gif)
解析
核心考点
试题【.设是椭圆上的两点,点是线段的中点,线段的垂直平分线与椭圆相交于两点.(1)确定的取值范围,并求直线的方程;(2)试判断是否存在这样的,使得四点在同一个圆上?并】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
在平面直角坐标系xoy中,椭圆E:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182047-58390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182048-29930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182048-75557.gif)
(Ⅰ)求椭圆E的方程;
(Ⅱ)设椭圆E与y轴的两
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182048-29403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182039-37550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182039-58894.gif)
(1)已知椭圆的长轴是短轴的
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182030-31298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182030-52946.gif)
(2)已知椭圆的中心在原点,以坐
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182030-75328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182031-87541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182031-62637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182022-69888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182023-42724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182023-38202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182023-88593.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182023-28489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182024-14198.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182024-35543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182024-74940.gif)
中
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182024-12364.gif)
1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182025-79028.gif)
2)若椭圆的离心率
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182025-34385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182025-62514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182019-12674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023182020-27849.gif)
A.9 | B.16 | C.7 | D.9或7 |
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