题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-30910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060803-64879.png)
(1)求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
(2)若圆
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060803-68173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060803-45176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060803-28404.png)
(3)圆
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-17421.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-52248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-21812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-96384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-12295.png)
解析
(2)可设直线MN的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-28134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-89927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-47583.png)
(3) 不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-95956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-37186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-78093.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-35574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-54919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-65097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-63136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-93447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-79784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-87095.png)
解:(1)依题设,圆
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-40839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-30743.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060809-65766.png)
得圆
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-52248.png)
(2)由题意,可设直线MN的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-28134.png)
则圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-89927.png)
由垂径分弦定理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-47583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060809-85375.png)
所以直线MN的方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-21812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060804-96384.png)
(3)不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-95956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-37186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-78093.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060806-35574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-54919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060809-89515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-63136.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060807-93447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-79784.png)
由于点
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060810-41378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060802-93254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060810-37515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060810-20426.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060808-87095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060805-12295.png)
核心考点
试题【(本小题满分12分) 在直角坐标系中,以坐标原点为圆心的圆与直线:相切.(1)求圆的方程;(2)若圆上有两点关于直线对称,且,求直线MN的方程;(3)圆与x轴相】;主要考察你对平面向量数量积的意义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060751-54932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060751-42844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060745-62464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060746-56703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060746-14737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060746-11030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060745-62464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060746-56703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060738-67071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060738-67147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060738-87822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060739-13471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060739-37392.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060733-95489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060733-88557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060733-32787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060733-58855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060734-31304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060734-99122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060733-95489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060734-43216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060727-39894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060727-83430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060727-33692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060728-60927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060728-62681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104060728-79924.png)
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