Problem Locus

The circle $x^{2} + y^{2} - 4x - 4y + 4$ is inscribed in a triangle whose two sides lie on the co-ordinate axes.The locus of the circumcenter of this triangle can be represented as $ax + by - cxy +k(\sqrt(x^{2} + y^{2})$ =0.Where a,b,c,d are real constants.

Find the value of a+b+c+k.