题目
题型:不详难度:来源:
矩形ABCD的对角线AC、BD相交于点M (2,0),AB边所在直线的方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150440-10226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150440-27666.png)
(1)求点A的坐标及矩形ABCD外接圆的方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150440-99626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-75964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-33829.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-20862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-59790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-39850.png)
解析
试题分析:(1)∵AC⊥AD 且
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-59840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-46649.png)
∴直线AD的方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-55932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150443-72147.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150443-61749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150443-61771.png)
∵ABCD是矩形 ∴ABCD外接圆的圆心为对角线AC与BD的交点,即M(2,0),
半径r="|AM|=2"
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150443-57851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-20862.png)
(2)①当直线m的斜率不存在时,其方程为x="0," m与圆M的交点为A(0,-2),B(0,2)
满足|AB|=4, ∴x=0符合题意。 ………8分
②当直线m的斜率存在时,设m的方程为y=kx-1,即kx-y-1=0,则圆心(2,0)到直线m的距离为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150444-26713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150444-63819.png)
∴此时m的方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-39850.png)
故所求m的方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150441-59790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150442-39850.png)
点评:典型题,涉及求圆的问题,往往利用定义法—即求圆心、半径,或利用“待定系数法”。本题中求切线方程是一道易错题,应该注意到,自圆外一点作圆的切线有两条,防止遗漏“斜率”不存在的切线。
核心考点
试题【(本小题满分12分)矩形ABCD的对角线AC、BD相交于点M (2,0),AB边所在直线的方程为:,若点在直线AD上.(1)求点A的坐标及矩形ABCD外接圆的方】;主要考察你对直线方程的几种形式等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150436-23010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150436-21072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150436-84205.png)
A.-8 | B.0 | C.4 | D.10 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150426-99276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150426-65657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150426-13320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150426-29224.png)
A.1或-2 | B.1 | C.-2 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150414-62564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150414-59122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150414-29639.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-58137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-58308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-20928.png)
(1) 直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-68151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150408-68721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-68151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150408-26484.png)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-68151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150408-26484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150407-68151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150408-77480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-99342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-63860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-90680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-46362.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-99342.png)
(2)已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150354-37628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150353-99342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022150354-45162.png)
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