If the normal at an end of a latus rectum passes through th…

Maths Conic Sections Ellipse Single Correct MCQ

Published on: August 14, 2026

If the normal at an end of a latus rectum passes through the extremity of the minor axis then eccentricity of the ellipse is given by

e 2 + e + 1 = 0

e 4 + e 2 + 1 = 0

e 4 – e 2 – 1 = 0

e 4 + e 2 – 1 = 0

Text Solution

Verified by Experts

The correct answer is:

Let equation of ellipse be

and L

be one end of a latus rectum through S(ae, 0)

Now equation of normal at L is ⇒ ⇒

⇒ ⇒

Now this normal passing through L’(0, b)

∴ ∴ b = ae 2 ⇒ ⇒ b

2 =a 2 e 4 ∴ ∴ a

2 (1 – e 2 ) = a 2 e 4 ⇒ ⇒ e

4 + e 2 – 1 = 0

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