JEE Main 2022MathematicsParabolaCommon TangentmediumNumerical

JEE Main 2022 — Parabola Question with Solution

From: JEE Main 2022 (Online) 26th June Morning Shift

Question

Let the common tangents to the curves and intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l respectively denote the eccentricity and the length of the latus rectum of this ellipse, then is equal to ______________.

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

Let y = mx + c is the common tangent

So

So equation of common tangents will be , which intersects at Q(3, 0)

Major axis and minor axis of ellipse are 12 and 6.

So eccentricity

and length of latus rectum

Hence,

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About this question

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