The locus of the centre of a circle of radius 2 which rolls on the outside of the circle x2+y2+3x−6y−9=0 , is

Let (h, k) be the coordinates of the centre of the circle which rolls on the outside of the circle  x2+y2+3x−6y−9=0 . Then ,Distance between centres = Sum of the radii  ⇒ h+322+(k−3)2=92+2⇒ h2+k2+3h−6k+94+9=92+2⇒ h2+k2+3h−6k−31=0 Hence, the locus of f(h,k) is  x2+y2+3x−6y−31=0