1.设圆的方程为(x-a)^2+(y-b)^2=r^2
a^2+b^2=r^2
(2-a)^2+b^2=r^2
|a+b-4|/√ 2=r
a=1或
b=-7
r=5√ 2
或
a=1
b=1
r=√ 2
圆的方程为(x-1)^2+(y-1)^2=2或(x-1)^2+(y+7)^2=50
2
圆系方程:
经过两圆x^2+y^2+D1x+E1y+F1=0,
x^2+y^2+D2x+E2y+F2=0的交点圆系方程为：
x^2+y^2+D1x+E1y+F1+λ(x^2+y^2+D2x+E2y+F2)=0 (λ≠-1)
解:
x^2+y^2-4x-6+λ(x^2+y^2-4y-6)=0
(1+λ)x^2-4x+(1+λ)y^2-4λy-6-6λ=0
(x-(2/(1+λ)))^2+(y-(2λ/(1+λ)))^2-(4+4λ^2)/(1+λ)^2-6-6λ=0
(2/(1+λ),2λ/(1+λ))在x-y-4=0上
x-y-4=0=>λ=-1/3
圆方程x^2-6x+y^2+2y-6=0