JEE Main 2021MathematicsParabolaEasyNumerical

JEE Main 2021 — Parabola Question with Solution

JEE Main 2021 (20 Jul Shift 2)

Question

If the point on the curve y2=6x, nearest to the point 3,32 is (α,β), then 2(α+β) is equal to _________.

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Show full solutionCorrect answer: 9
Correct answer
9

Step-by-step explanation

We have,

y2=6x

Comparing with y2=4ax, we get a=32

Let the point on parabola be P≡at2,2at≡32t2,3t.

Normal at point P is

tx+y=3t+32t3

It passes through 3,32, hence

⇒3t+32=3t+32t3

⇒t3=1⇒t=1

Hence,

P≡32,3=(α,β)

Therefore,

2(α+β)=232+3=9

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About this question

This is a previous-year question from JEE Main 2021, 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.