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Q.

If P and Q are the lengths of the perpendiculars from the origin to the lines  x cos θ + y sin θ = k cos 2 θ and x sec θ – y cosec θ = k respectively then

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a

p2-4q2=k2

b

p2+4q2=k2

c

4p2+4q2=k2

d

p2+q=k2

answer is B.

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Detailed Solution

p=|kcos⁡2θ|cos2⁡θ+sin2⁡θ=|kcos⁡2θ|q=|k|sec2⁡θ+coses2⁡θ=|ksin⁡θcos⁡θ|  =|k(1/2)sin⁡2θ|So p2+4q2=k2cos2⁡2θ+sin2⁡2θ=k2.
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If P and Q are the lengths of the perpendiculars from the origin to the lines  x cos θ + y sin θ = k cos 2 θ and x sec θ – y cosec θ = k respectively then