# If p1 and p2 are the lengths of the perpendiculars form the origin upon the lines x sec θ + y cosec θ = a and x cos θ – y sin θ = a cos 2 θ respectively, thenA. 4p12 + p22 = a2B. p12 + 4p22 = a2C. p12 + p22 = a2D. none of these

The given lines are

x sec θ + y cosec θ = a … (1)

x cos θ y sin θ = a cos 2 θ … (2)

p1 and p2 are the perpendiculars from the origin upon the lines (1) and (2), respectively.

4p12 + p22 = a2 (sin2 2θ + cos2 2 θ) = a2

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