Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Show that the normal at any point θ to the curve x = a (cos θ + θ sin θ ), y = a (sin θ – θ cos θ ) is at a constant distance from the origin.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. 
= a(–sin θ + θ cos θ + sin θ )
= a θ cos θ
= a(cos θ –cos θ + θ sin θ )
= a θ sin θ
= tan θ
equation of normal is
y –a(sin θ – θ cos θ ) = 
[x –a (cos θ + θ sin θ )
⇒ x cos θ + y sin θ = a
Length of ⊥ from (0, 0) is
p = 
p = a which is constant.
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