Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The normal at a variable point P on an ellipse 
= 1 of eccentricity 'e' meets the axes of the ellipse in Q and R then the locus of the mid-point of QR is a conic with an eccentricity e' such that -
Text Solution
Verified by ExpertsThe correct answer is:
B
Equation of normal at P ≡ (a cos θ , b sin θ )
is 
– 
= a 2 – b 2 Q ≡ 
R ≡ 
∴ M = 
≡ (h, k)
Hence locus of M
+ 
= 1
which is an ellipse with eccentricity e ′
a > b ⇒ 4a
2 > 4b 2 ⇒ 
< 
⇒ 
< 
= 
(1 – e ′
2 ) ⇒ b 2 = a 2 (1 – e ′ 2 )
⇒ e = e ′
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