JEE Main 2020MathematicsParabolaHardNumerical

JEE Main 2020 — Parabola Question with Solution

JEE Main 2020 (08 Jan Shift 2)

Question

Let a line y=mxm>0, intersect the parabola, y2=x, at a point P, other than the origin. Let the tangent to it a P, meet the x-axis at the point Q. If area ΔOPQ=4 square unit, then m is equal to

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Show full solutionCorrect answer: 0.5
Correct answer
0.5

Step-by-step explanation


Let the equation of tangent at P is 2ty=x+t2
So, Q-t2,0

As given, area ΔOPQ=4 square unit, so
12001t2t1-t201=±4
t3=±8
t=2 t>0

So, m=tt2=12.

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About this question

This is a previous-year question from JEE Main 2020, 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.