If a circle passes through (a, b)and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is

Let the equation of the circle bex2+y2−2gx−2fy+c=0. As it passes through (a, b)         a2+b2−2ga−2fb+c=0Since it intersects the circle x2+y2=4 orthogonally            2g×0+2f×0=c−4⇒c=4and the locus of (g,f), the centre is        2ax+2by−a2+b2+4=0