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CGP EDU Academic Team
Published on: August 13, 2026
If p and p´ be the perpendiculars from the origin upon the straight lines whose equations are x sec θ + y cosec θ = a and x cos θ – y sin θ = a cos 2 θ then prove that 4p 2 + p´ 2 = a 2
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. p = length of ⊥ from (0, 0) to x sec θ + y cosec θ – a 2 = 0
⇒ p = 
= 
= a sin θ cos θ ⇒ 2p = a(2 sin θ cos θ ) = a sin 2 θ ...(1)
and p´ = length of the perpendicular from (0, 0) to
x cos θ – y sin θ – a cos 2 θ = 0
⇒ p´ = 
= a cos 2 θ ...(2)
Now 4p 2 + p' 2 = a 2 sin 2 2 θ + a 2 cos 2 2 θ = a 2
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