If a circle passes through (1, 2) and cuts the circle x2 + y2 = 4 orthogonally then the equation of the locus of its centre, is

Let the circle be x2+y2+2gx+2fy+c=0. This passes through (1, 2) and cuts the circle x2+y2=4 orthogonally.∴ 5+2g+4f+c=0 …(i) and, 0=c−4      ...(ii)Eliminating c from (i) and (ii), we get       2g+4f+9=0.Hence the locus of the centre (- g, - f ) is    −2x−4y+9=0 or, 2x+4y−9=0