Answer :

Given lines are xcosθ -ysinθ = -kcos2θ

And xsecθ +ycosecθ =k

Now, we find perpendicular of these lines from the origin

P = and q=

P=kcos2θ and q = kcosθ sinθ

P=kcos2θ and q =

Cos2θ = , q= i.e. sin2θ =

Since cos^{2}2θ +sin^{2}2θ =1

We have,

Or p^{2}+4q^{2}=k^{2}

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