题目
题型:不详难度:来源:
已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233704-70518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233704-72794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-67635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-78163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-25001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233706-23660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233706-49858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-76828.png)
(1)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-47074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-36484.png)
(2)斜率为1的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-19041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-36484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233708-63868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233708-95286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233708-73010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-19041.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-42211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-20382.png)
解析
(1)因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233704-70518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233704-72794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-67635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-78163.png)
原点对称.线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-25001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233706-23660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233706-49858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233707-76828.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-14963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-63366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-70691.png)
解:(1)由题意得,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233710-65349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233705-78163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233710-49525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233710-93406.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233710-38929.png)
∴ 点M的轨迹是以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233711-90309.png)
其中长轴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233711-87398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233711-84688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233711-91719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233712-67677.png)
椭圆方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-42211.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-14963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-63366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-70691.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233712-98757.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233712-88347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233712-67330.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233713-69276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233713-61141.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233708-95286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233713-34965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233713-47439.png)
整理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233714-76142.png)
化简可得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233714-48625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-14963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233709-20382.png)
核心考点
试题【(本小题满分12分)已知点是圆上任意一点,点与点关于原点对称.线段的中垂线分别与交于两点.(1)求点的轨迹的方程;(2)斜率为1的直线与曲线交于两点,若(为坐标】;主要考察你对点到直线的距离等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233658-39766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233658-93326.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233658-39766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233658-39766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233654-70337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233654-15045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-99401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-73164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-49535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233647-86884.png)
(1)求圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-73164.png)
(2)若圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-73164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233646-73164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233636-73579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233636-50784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233636-93991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233631-57638.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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