If the length of the tangent from $(h,k)$ to the circle $x^2+y^2=16$ is twice the length of the tangent from the same point to the circle $x^2+y^2+2x+2y=0,$ then

Question

\[(a)\;h^2+k^2+4h+4k+16=0 \quad (b)\;h^2+k^2+3h+3k=0 \quad (c)\;3h^2+3k^2+8h+8k+16=0 \quad (d)\;3h^2+3k^2+4h+4k+16=0 \]