题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151200-25077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151200-29176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151201-21201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151201-13070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151202-31505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151202-43533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-14835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-77339.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151200-25077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-71104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-62413.png)
(2)若圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-72717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-71104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-21750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-65192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-23772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
(3)问圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-65192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-68467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-68467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-47693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-47693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-68467.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-35927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-82743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-61156.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-11013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-57212.png)
解析
试题分析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151202-43533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-14835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151203-77339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-66336.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151207-51333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-82743.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151207-97913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151201-21201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151207-39288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151202-31505.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151207-17674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-35927.png)
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151200-29176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-35927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151201-21201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-20966.png)
注意到
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-25605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-85718.png)
设圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-85636.png)
因为圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-20966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151208-40683.png)
又因为斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-65192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151204-30016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151205-23772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151209-14894.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151209-96837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151209-43754.png)
由①②解得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151209-36399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-40371.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-48589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-13739.png)
所以所求圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-61156.png)
(3)假设存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-11476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-11476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151210-11003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151211-33755.png)
联立方程
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151211-74193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151211-22753.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151211-88947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151212-87966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151212-81221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151212-36641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151212-23894.png)
依题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151213-63964.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151213-87797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151213-24907.png)
经验证,满足题意。故所求直线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-11013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151206-57212.png)
点评:此题主要考查了直线与圆的位置关系,涉及的知识较多,综合性较强。知识点的灵活应用是解题的关键,是一道中档题。
核心考点
试题【已知的顶点,边上的中线所在的直线方程为,边上的高所在直线的方程为。(1)求的顶点、的坐标;(2)若圆经过不同的三点、、,且斜率为的直线与圆相切于点,求圆的方程;】;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/20191022/20191022151155-10370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151155-82919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151155-18449.png)
A.![]() | B.![]() | C.0,![]() | D.0,![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151150-17987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151151-16631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151142-94840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151142-66204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151142-39736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151142-65694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151142-93735.png)
A.x-2y-1=0 | B.x-2y+1="0" | C.2x+y-2=0 | D.x+2y-1=0 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151135-82877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022151135-10233.png)
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