JEE Main 2016MathematicsParabolaMediumMCQ

JEE Main 2016 — Parabola Question with Solution

JEE Main 2016 (10 Apr Online)

Question

P and Q are two distinct points on the parabola, y2=4x, with parameters t and t1, respectively. If the normal at P passes through Q, then the minimum value of t12 , is

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Show full solutionCorrect option: A
Correct answer
A8

Step-by-step explanation

Given Pt2, 2t and Qt12, 2t1, are parametric points on parabola
y2=4x
Slope of normal at P=-t

Since normal passes through Q, 

⇒  slope of normal at P = slope of PQ

⇒ -t=2t1-tt12-t2

⇒ -t=2t1+t

⇒t1=-t-2t

⇒t12=t2+4t2+4   ...1

t2+4t2≥2t2.4t2≥4,

Using AM≥GM

∴  t12≥4+4   from 1

⇒ t12≥8

∴   Minimum value=8

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About this question

This is a previous-year question from JEE Main 2016, 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.