设圆方程为 (x-a)^2+(y-b)^2=r^2,点A、B在圆上,满足圆方程:
(-1-a)^2+(1-b)^2=r^2 (1)
(5-a)^2+(1-b)^2=r^2 (2)
(2)-(1)
(a+1)^2=(a-5)^2 两边开平方 a+1=a-5(舍去) a+1=5-a 2a=4 a=2
圆心(a,b)与M(3.2)连线与L:x+y-5=0垂直,故两斜率乘积为-1
(b-2)/(a-3)*(-1)=-1 (3)
b-2=a-3 b=a-1
=2-1
=1
所以圆心坐标(2,1)代入(1)
(2+1)^2+(1-1)^2=r^2 r=3
圆c方程为 (x-2)^2+(y-1)^2=9