题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221832-98992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221832-98204.png)
求:(1)求圆的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-71260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-73863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
(3)在(2)的条件下,是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-46390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-66581.png)
若存在,求出实数
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-17323.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-93383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-93524.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221835-78677.png)
解析
试题分析:(1)设圆心为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221835-97261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-32622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-71260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
(3)根据圆的几何性质,垂直平分弦
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-46527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-17323.png)
试题解析:(1)设圆心为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221835-97261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-32622.png)
由于圆与直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-42315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-87912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221837-36896.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221837-66637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221837-77141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221837-20137.png)
故所求的圆的方程是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-93383.png)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221838-10577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221838-62598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221838-76685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221838-39862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221838-10577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-73863.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221839-86289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221839-97276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221839-34782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221839-98096.png)
所以实数
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-93524.png)
(3)设符合条件的实数
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-69549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221840-89963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221840-26718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221840-97088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221840-88167.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221836-46527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221840-87978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221841-70952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221835-78677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221841-57716.png)
所以存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221835-78677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-46390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221833-98875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221834-66581.png)
核心考点
试题【已知半径为5的圆的圆心在轴上,圆心的横坐标是整数,且与直线相切.求:(1)求圆的方程;(2)设直线与圆相交于两点,求实数的取值范围;(3)在(2)的条件下,是否】;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/20191022/20191022221825-59782.png)
①截y轴所得弦长为2;
②被x轴分成两段圆弧,其弧长的比为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221825-26051.png)
求在满足条件①②的所有圆中,使代数式
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221825-20331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221818-97684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221818-14147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221819-20994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221819-63216.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221810-75025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221811-16934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221811-30311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221811-24324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221811-28535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221801-28858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221801-42709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221802-93380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221802-99147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221754-80448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221754-62073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022221754-20706.png)
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