JEE Main 2020MathematicsParabolaHardMCQ

JEE Main 2020 — Parabola Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

For a>0, let the curves C1:y2=ax and C2:x2=ay intersect at origin O and a point P. Let the line x=b0<b<a intersect the chord OP and the x -axis at points Q and R, respectively. If the line x=b bisects the area bounded by the curves, C1 and C2, and the area of ∆OQR=12, then ‘ a ’ satisfies the equation:

Choose an option

Show full solutionCorrect option: B
Correct answer
Bx6-12x3+4=0

Step-by-step explanation

∫0bax-x2adx=a26

⇒ 23ab32-b33a=a26           ...1

Also area of ΔOQR=12 

12b2=12⇒b=1

Put in 1

⇒ 4aa-2=a3

⇒ a6+4a3+4=16a3

⇒ a6-12a3+4=0

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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.