Locus Problem

Geometry Level 3

The circle $$x^2+y^2-4x-4y+4=0$$ is inscribed in a triangle which has two of its sides along the coordinate axes. The locus of the circumcentre of the triangle is $$x+y-xy+k(x^2+y^2)^{1/2}=0$$. Find $$k$$.

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