Question

求过点P(-8,-1)Q(5,12)R(17,4)三点的圆的圆心坐标

Answer 1

设圆心为(x,y)

圆心到这3个点距离相等

(x+8)²+(y+1)²=(x-5)²+(y-12)²=(x-17)²+(y-4)²

16x+64+2y+1=-10x+25-24y+144=-34x+289-8y+16

16x+2y+65=-10x-24y+169=-34x-8y+305

{16x+2y+65=-10x-24y+169

-10x-24y+169=-34x-8y+305

解得：

{x=5

y=-1

圆心(5,-1)