求经过坐标原点和点P(1，1)，并且圆心在直线2x＋3y＋1＝0上的圆的方程

问题详情：

求经过坐标原点和点P(1，1)，并且圆心在直线2x＋3y＋1＝0上的圆的方程____________．

【回答】

 (x－4)2＋(y＋3)2＝25.

解析：设圆心为C(x，y)．显然，所求圆的圆心在OP的垂直平分线上，OP的垂直平分线方程为＝，即x＋y－1＝0.

解方程组得圆心C的坐标为(4，－3)．                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

又圆的半径r＝|OC|＝5，

∴所求圆的方程为(x－4)2＋(y＋3)2＝25.

知识点：圆与方程

题型：填空题