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

For the given circle, the centre is (−3/2,3)  and radius =(9/4+9+9)=9/2 . Obviously the locus of the centre of the circle which rolls is also a circle having the same centre (−3/2,3)  and radius =(9/2)+3=15/2 .∴     the required locus is (x+3/2)2+(y−3)2=(15/2)2 or    x2+y2+3x−6y−45=0 .