JEE Main 2019MathematicsParabolaHardMCQ

JEE Main 2019 — Parabola Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

Let A4,-4 and B9,6 be points on the parabola, y2=4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ΔACB is maximum. Then, the area (in sq. units) of ΔACB , is:

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Show full solutionCorrect option: D
Correct answer
D3114

Step-by-step explanation

Let the coordinates of C be t2, 2t.

Area of ∆ABC=12 t22t19614-41



∆=56+t-t2, t∈-2, 3

d∆dt=1-2t=0⇒t=12

d2△dt2=-2, hence area is maximum at t=12

∴    Δmax=1254=3114

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About this question

This is a previous-year question from JEE Main 2019, 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.