设圆的方程为(X^2+y^2-4x-3)+ m(x^2+y^2-4y-3)=0
即:(1+m)X^2+(1+m)y^2-4X-4mY-3(1+m)=0
圆心为2/(1+m),2m/(1+m)
带入X-Y-4=0,解得m=-1/3
再带入(X^2+y^2-4x-3)+ m(x^2+y^2-4y-3)=0即可