JEE Main 2022MathematicsParabolaMediumMCQ

JEE Main 2022 — Parabola Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let x=2t,y=t23 be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then limt→1k is equal to

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Show full solutionCorrect option: D
Correct answer
D1318

Step-by-step explanation

The parametric form x=2t,y=t23 represents the parabola x2=12y

 

Given AS⊥AB

So, mAS·mAB=-1

⇒3-t230-2t·α-t230-2t=-1

 ⇒3α=27t2+t4t2-9

Ordinate of centroid of ΔSAB=k=α+t23+33=9+3α+t29

limt→1k=limt→1199+t2+27t2+t4t2-9=1318

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About this question

This is a previous-year question from JEE Main 2022, 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.