JEE Main 2015MathematicsEllipseMediumMCQ

JEE Main 2015 — Ellipse Question with Solution

JEE Main 2015 (04 Apr)

Question

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the ellipse x29+y25=1, is

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Show full solutionCorrect option: A
Correct answer
A27

Step-by-step explanation

x29+y25=1

e=1-59=23

a2=9, b2=5

Foci =±ae,0=±2,0

Ends of latus rectum=±ae,±b2a

=±2,±53

Tangent at 'L' is T=0

2×x9+53×y5=1

It cuts coordinate axes at P92,0 & Q0,3

Area of quadrilateral PQRS=4 (Area of triangle OPQ)

=4 12×92×3=27 sq. units

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About this question

This is a previous-year question from JEE Main 2015, 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.