JEE Main 2019MathematicsEllipseMediumMCQ

JEE Main 2019 — Ellipse Question with Solution

JEE Main 2019 (08 Apr Shift 2)

Question

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at 0,53, then the length of its latus rectum is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D5

Step-by-step explanation


Given, difference of the lengths of major and minor axis is 10.
⇒2b-2a=10 … (1)
One of the focii is 0, 53
⇒be=53 … (2)
Also a2=b21-e2 .......(3)
⇒a2=b2-75
⇒b-aa+b=75
⇒a+b=15 … (4)
From (1) and (4)
a=5 and b=10
Hence length of the latus rectum =2a2b=2⋅2510=5

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 2019, 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.