The equation of a circle `C_1` is `x^2+y^2-4x-2y-11=0` A circle`C_2` of radius `1` rolls on the outside of the circle `C_1` The locus of the centre `C_2` has the equation

Options

A. `x^(2)+y^(2)-4x-2y-20=0`
B. `x^(2)+y^(2)+4x+2y-20=0`
C. `x^(2)+y^(2)-3x-y-11=0`
D. none of these

Answer

A

Explanation

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`.