Question

設(shè)圓上的點(diǎn)A(2,3)關(guān)于直線x+2y=0的對(duì)稱點(diǎn)仍在這個(gè)圓上,且與直線x-y+1=0相交的弦長為22,求圓的方程.

Answer 1

(x+6)²+(y-3)²=64或(x+14)²+(y-7)²=272.?

解析:點(diǎn)A(2,3)關(guān)于直線x+2y=0的對(duì)稱點(diǎn)在本圓上,圓心在該直線上,?

∴設(shè)圓方程為(x-a)²+(y-b)²=r².?

                            ①

(2-a)²+(3-b)²=r².                                     ②?

a+2b=0.                                                   ③?

解①②③得