JEE Main 2024MathematicsParabolaMediumMCQ

JEE Main 2024 — Parabola Question with Solution

JEE Main 2024 (30 Jan Shift 1)

Question

The maximum area of a triangle whose one vertex is at (0,0) and the other two vertices lie on the curve y=-2x2+54 at points (x, y) and (-x, y) where y>0 is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D108

Step-by-step explanation

Let, area of triangle ABC be denoted by P.

⇒P=12001xy1-xy1

⇒P=120-0+2xy

⇒P=xy

⇒P=x-2x2+54

⇒P=-2x3+54x

⇒dPdx=-6x2+54

For critical points, dPdx=0

⇒-6x2+54=0

⇒x=±3

So, the maximum area will be,

A=3(-2×9+54)

⇒A=108

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About this question

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