JEE Main 2024MathematicsEllipseHardMCQ

JEE Main 2024 — Ellipse Question with Solution

JEE Main 2024 (01 Feb Shift 2)

Question

Let P be a point on the ellipse x29+y24=1. Let the line passing through P and parallel to y-axis meet the circle x2+y2=9 at point Q such that P and Q are on the same side of the x-axis. Then, the eccentricity of the locus of the point R on PQ such that PR:RQ=4:3 as P moves on the ellipse, is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D137

Step-by-step explanation

Given equation of ellipse and circle are x29+y24=1 and x2+y2=9.

⇒P≡3cosθ, 2sinθ and Q≡3cosθ, 3sinθ

Let, R≡h,k

⇒h=3cosθ, k=187sinθ

⇒h3=cosθ, 7k18=sinθ

So, locus of R is given by, x29+49y2324=1.

⇒e=1−32449×9

⇒e=11721

⇒e=137

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About this question

This is a previous-year question from JEE Main 2024, 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.