求經過座標原點和點P(1，1)，並且圓心在直線2x＋3y＋1＝0上的圓的方程

問題詳情：

求經過座標原點和點P(1，1)，並且圓心在直線2x＋3y＋1＝0上的圓的方程____________．

【回答】

 (x－4)2＋(y＋3)2＝25.

解析：設圓心為C(x，y)．顯然，所求圓的圓心在OP的垂直平分線上，OP的垂直平分線方程為＝，即x＋y－1＝0.

解方程組得圓心C的座標為(4，－3)．                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

又圓的半徑r＝|OC|＝5，

∴所求圓的方程為(x－4)2＋(y＋3)2＝25.

知識點：圓與方程

題型：填空題