题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233342-73334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233342-14433.png)
(1)证明:不论m取何值,直线l与圆C恒相交;
(2)求直线l被圆C截得的弦长最短时的直线方程.
答案
解析
解:由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233342-73334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233343-42965.png)
∴圆C的圆心为(2,3),半径为2……………2分
(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233342-14433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233343-95919.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233343-95208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233343-37131.png)
∴不论m取何值,直线l恒过点P(3,2)…………….4分
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233343-92969.png)
∴点P(3,2)在圆C内……………3分
所以不论m取何值,直线l与圆C恒相交…………….5分
(2)当直线l垂直CP时,直线l被圆C截得的弦长最短
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233344-68153.png)
所以所求的直线方程为y=x-1…………….8分
核心考点
举一反三
(1)求圆C的方程;
(2)设直线ax-y+1=0与圆C交于A,B两点,是否存在实数a,使得过点P(2,0)的直线l垂直平分弦AB?若存在,求出实数a的值;若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233325-52057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-96956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-59519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-52539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-41834.png)
(Ⅰ)判断直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233325-52057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-52539.png)
(Ⅱ)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-20705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233326-52539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233327-33451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233327-39496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-55294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-12995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-35846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-71458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233322-84314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233322-67061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-71458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233322-84314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233321-55294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233322-66785.png)
A.![]() | B.![]() | C.![]() | D.![]() |
在平面直角坐标系xOy中,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233315-33892.png)
(Ⅰ)求圆C的方程;
(Ⅱ)若圆C被直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233315-86054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233316-12872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233316-35496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233310-65096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233311-73276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022233311-18260.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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