Question

If P₁ and P₂ are the lengths of the perpendiculars form the origin upon the lines x secθ + y cosec θ = a and x cos θ – y sin θ = a cos 2 θ respectively, then 

A. 4p₁² + p₂² = a² 

B. p₁² + 4p₂² = a²

C. p₁² + p₂² = a² 

D. none of these

Answer 1

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 (sin²2θ + cos²2 θ) = a²