If $p$ and $q$ are the perpendicular distance from the origin to the straight lines $x\; \sec \theta-y \;cosec \theta=a$ and $x \cos \theta+ y \sin \theta= a \cos 2 \theta,$ then

Question

\[(a)\;4p^2+q^2=a^2 \quad (b)\;p^2+q^2=a^2 \quad (c)\;p^2+2q^2=a^2 \quad (d)\;4p^2+q^2=a^2\]