If \( p \) and \( q \) are the lengths of perpendiculars from the o...

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If \( p \) and \( q \) are the lengths of perpendiculars from the origin to the lines \( x \cos \theta-y \sin \theta=k \cos 2 \theta \) and \( x \sec \theta+y \operatorname{cosec} \theta=k \), respectively, prove that \( p^{2}+4 q^{2}=k^{2} \).
\( \mathrm{P} \)
W.
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