JEE Main 2018MathematicsEllipseMediumMCQ

JEE Main 2018 — Ellipse Question with Solution

JEE Main 2018 (16 Apr Online)

Question

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 32 units, then its eccentricity is

Choose an option

Show full solutionCorrect option: D
Correct answer
D13

Step-by-step explanation

Given length of latus-rectum of an ellipse is 2b2a=4⇒b2=2a and  a-ae=32⇒a1-e=32.

Now we know, b2=a21-e2

⇒b2=a1-ea1+e

⇒2a=32a1+e  ∵  a1-e=32

⇒43=1+e

⇒e=13.

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About this question

This is a previous-year question from JEE Main 2018, covering the Ellipse chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.