JEE Main 2019MathematicsEllipseMediumMCQ

JEE Main 2019 — Ellipse Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

Let S=x,y∈R2:y21+r-x21-r=1, where r≠±1. Then S represents:

Choose an option

Show full solutionCorrect option: C
Correct answer
CAn ellipse whose eccentricity is 2r+1, when r>1

Step-by-step explanation

Given y21+r-x21-r=1

If r∈0,1 then this curve is a hyperbola whose eccentricity is 1+1-r1+r=2r+1. 

If r>1 , then this curve is an ellipse whose
eccentricity is 1-r-1r+1=2r+1. 

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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.