Correct Answer - A
Let (h,k) be the coordinates of the centre of circle `C_(2)` . Since circle `C_(2)` rolls on the outside of circle `C_(1)`.
`:.` Distance between the centres = Sum of the radii
`rArr sqrt((h-2)^(2)+(k-1)^(2))=1+4`
`rArr h^(2)+k^(2)-4h-2k-20=0`
Hence, the locus of (h, k) is `x^(2)+y^(2)-4x-2y-20=0`.