设所求圆的方程为x 2+y 2+2x+8y-8+λ(x 2+y 2-4x-4y-2)=0,
整理得(1+λ)x 2+(1+λ)y 2+(2-4λ)x+(8-4λ)y-8-2λ=0,
∴圆心坐标为(
2λ-1
1+λ ,
2λ-4
1+λ ),
∵圆心在直线x-y-4=0上,
∴
2λ-1
1+λ -
2λ-4
1+λ -4=0,解得:λ=-
1
4 ,
∴所求的圆的方程为x 2+y 2+4x+12y-10=0.
设所求圆的方程为x 2+y 2+2x+8y-8+λ(x 2+y 2-4x-4y-2)=0,
整理得(1+λ)x 2+(1+λ)y 2+(2-4λ)x+(8-4λ)y-8-2λ=0,
∴圆心坐标为(
2λ-1
1+λ ,
2λ-4
1+λ ),
∵圆心在直线x-y-4=0上,
∴
2λ-1
1+λ -
2λ-4
1+λ -4=0,解得:λ=-
1
4 ,
∴所求的圆的方程为x 2+y 2+4x+12y-10=0.