If a circle passes through $(a, b)$and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

Let the equation of the circle be
$x^2+y^2-2gx-2fy+c=0.$ As it passes through $(a, b)$
         $a^2+b^2-2ga-2fb+c=0$
Since it intersects the circle $x^2+y^2=4$ 
orthogonally  
          $2g\times 0+2f\times 0=c-4\Rightarrow c=4$
and the locus of $(g,f),$ the centre is
        $2ax+2by-\left(a^2+b^2+4\right)=0$