If $p$ and $q$ are the lengths of the perpendiculars from the origin on the lines, $x \operatorname { cosec } \alpha - y \sec \alpha = k \cot 2 \alpha$ and $x \sin \alpha + y \cos \alpha = k \sin 2 \alpha$ respectively, then $k ^ { 2 }$ is equal to $:$\\
(1) $2 p ^ { 2 } + q ^ { 2 }$\\
(2) $p ^ { 2 } + 2 q ^ { 2 }$\\
(3) $4 q ^ { 2 } + p ^ { 2 }$\\
(4) $4 p ^ { 2 } + q ^ { 2 }$