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