题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-44547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-87895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-83766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-95822.png)
(1)求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-83766.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-71585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-83766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-37117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-38695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-71585.png)
(3)问是否存在斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-65569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231323-83766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-20267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-20267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-78096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-79804.png)
解析
试题分析:(1)因为O点到直线x﹣y+1=0的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231326-29172.png)
所以圆O的半径为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231326-12975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-78096.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-71585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231326-50713.png)
由直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231324-71585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231326-29918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231327-85394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231327-91825.png)
当且仅当a=b=2时取等号,此时直线l的方程为x+y﹣2=0 8分
(3)设存在斜率为2的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231327-68629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231327-72510.png)
则:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231327-96670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231328-17700.png)
依题意得;
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231328-49101.png)
因为以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-20267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231328-60459.png)
所以有:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231328-52292.png)
所以存在斜率为2的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-55084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231325-79804.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。熟练掌握定理及法则以及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【平面直角坐标系中,直线截以原点为圆心的圆所得的弦长为(1)求圆的方程;(2)若直线与圆切于第一象限,且与坐标轴交于,当长最小时,求直线的方程;(3)问是否存在斜】;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/20191022/20191022231316-91575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231316-17181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231316-12754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231316-12754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231316-87517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231316-17181.png)
如图,已知C、F是以AB为直径的半圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-10718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-48585.png)
(Ⅰ)证明:CD为圆O的切线;
(Ⅱ)若AD=3,AB=4,求AC的长.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-45370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-56968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-32128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-51599.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-98546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-22698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-91878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-49280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-66952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-16591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-67798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231251-89967.png)
(1)求证:直线和圆相交
(2)当圆截直线所得弦最长时,求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231251-31718.png)
(3)直线将圆分成两个弓形,当弓形面积之差最大时,求直线方程
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