The centre of circle S  lies on 2x−2y+9=0  and it cuts orthogonally the circle x2+y2=4 . Then the circle passes through two fixed points:

Let S'=x2+y2+2gx+2fy+c=0 . Centre (−g,−f)  lies on 2x−2y+9=0 .∴       −2g+2f+9=0 .S  cuts the circle x2+y2−4=0 orthogonally,∴      C−4=0 .∴    S=x2+y2+(2f+9)x+2fy+4=0 ⇒     S=(x2+y2+9x+4)+2f(x+y)=0 Every member of this family passes through the points of intersection ofx2+y2+9x+4=0  and x+y=0 i.e., through the points (−1/2,1/2)  and (−4,4) .