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MBA-MBA联考-考试常用数学公式-几何“圆”部分

发布时间：2016-04-22　来源：高仕教育　浏览数：0　

（四）圆（到某定点的距离相等的点的轨迹）
1、圆的标准方程：

2、圆的一般方程式

其中半径

，圆心坐标

思考：方程

在

和

时各表示怎样的图形？
3、关于圆的一些特殊方程：
（1）已知直径坐标的，则：若

，则以线段AB为直径的圆的方程是

（2）经过两个圆交点的，则：
过

的交点的圆系方

（3）经过直线与圆交点的，则：
过

与圆

的交点的圆的方程是：

（4）过圆切点的切线方程为：

重要推论（已知曲线和切点求其切线方程——就是把其中的一个

替换后代入原曲线方程即可）：
例如，抛物线

的以点

为切点的切线方程是：

，即：

。
1、直线与圆的位置关系

相交

相切

相离

最常用的方法有两种，即：
（1）判别式法：Δ>0，=0，<0，等价于直线与圆相交、相切、相离；

（2）考查圆心到直线的距离与半径的大小关系：距离大于半径、等于半径、小于半径，等价于直线与圆相离、相切、相交。
2、两个圆的位置关系

相交

外切

相离

试听预约

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