JEE Main 2022MathematicsEllipseMediumMCQ

JEE Main 2022 — Ellipse Question with Solution

JEE Main 2022 (29 Jun Shift 1)

Question

Let PQ be a focal chord of the parabola y2=4x such that it subtends an angle of π2 at the point 3,0. Let the line segment PQ be also a focal chord of the ellipse E:x2a2+y2 b2=1,a2>b2. If e is the eccentricity of the ellipse E, then the value of 1e2 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B3+22

Step-by-step explanation

Since PQ is focal chord of the parabola y2=4ax

so let Pt2,2t, Q1t2,-2t and R3,0

Given mPR·mPQ=-1

2tt2-3×-2t1t2-3=-1

t2-12=0

⇒t=1

i.e. PQ must be the latus rectum

We get P1,2 & Q1,-2

For ellipse

2b2a=4 & ae=1

Also b2=a21-e2

∴ a=1+2

and e2=3-22

Hence 1e2=13-22=3+22

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About this question

This is a previous-year question from JEE Main 2022, 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.