JEE Main 2018 — Ellipse Question with Solution
From: JEE Main 2018 (Online) 16th April Morning Slot
Question
If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is units, then its eccentricity is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
If the cordinate of focus and vertex are (ae, 0) and (a, 0) respectively,
then distance between focus and vertex,
a ae = (given)
a (1 e) =
Length of latus rectum,
b2 = 2a
a2(1 e2) = 2a [As b2 = a2 (1 e2)]
a (1 e) ( 1 + e) = 2
Putting a (1 e) =
(1 + e) = 2
3 + 3e = 4
e =
then distance between focus and vertex,
a ae = (given)
a (1 e) =
Length of latus rectum,
b2 = 2a
a2(1 e2) = 2a [As b2 = a2 (1 e2)]
a (1 e) ( 1 + e) = 2
Putting a (1 e) =
(1 + e) = 2
3 + 3e = 4
e =
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Ellipse chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →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.