Suppose ax + by + c = 0, where a , b and c are in AP be normal to a family of circles. The equation of the circle of the family intersecting the circle $x^2+y^2-4x-4y-1=0$  orthogonally is

a, b, and c are in AP. So, ax + by + c = 0 represents a family of lines passing through the point (1,-2). So, the family of circle (concentric) will be given by $x^2+y^2-2x+4y+c=0$ . It intersects the given circle orthogonally. Therefore,  $2(-1\times -2)+(2\times -2)=-1+corc=-3$