Let the equation of the circle is x2+y2+2gx+2fy+c=0 Centre is (−g,−f) since the circle passes through the point (0,2) . 4+0+4g+0+c=0 4+4g+c=0 And circle also touches the X-axis. g2=c Substitute the values 4+4g+g2=0 (g+2)2=0 g=−2 and c=4 This circle also cuts the circle x2+y2−2x−2y−2=0 orthogonally 2g1g2+2f1f2=c1+c2 2(−2)(−1)+2f(−1)=4−2 f=1 Hence the coordinate of the centre of the circle is (2,-1) .