If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec \alpha - y sec \alpha = k cot 2\alpha and x sin\alpha + y cos\alpha = k sin2\alpha respectively, then k2 is equal to :

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Answer: A. 4p2 + q2 First line is {x \over {\sin \alpha }} - {y \over {\cos \alpha }} = {{k\cos 2\alpha } \over {\sin 2\alpha }} \Rightarrow x\cos \alpha - y\sin \alpha = {k \over 2}\cos 2\alpha \Rightarrow p = \left| {{k \over 2}\cos \alpha } \right| \Rightarrow 2p = \left| {k\cos 2\alpha } \right| .... (i) second line is x\sin \alpha + y\cos \alpha = k\sin 2\alpha \Rightarrow q = \left| {k\sin 2\alpha } \right| .... (ii) Hence, 4{p^2} + {q^2} = {k^2} (From (i) & (ii))

If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$ respectively, then k2 is equal to :

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