Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find common normals of the curves y = 
and x 2 + y 2 – y = 0
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
for y = 
is 
= 
equation of normal is 
= 
⇒ 2y – 
= h 3 x – h 4
it passes from 
⇒ 1 – 
= – h 4 ⇒ h 6 + h 2 – 2 = 0
⇒ (h 2 – 1) (h 4 + h 2 + 2) = 0 ⇒ h = ± 1
⇒ common normals are x – 2y + 1 = 0 or 2y + x – 1 = 0
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