JEE Main 2023MathematicsParabolaHardMCQ

JEE Main 2023 — Parabola Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

Let PQ be a focal chord of the parabola y2=36x of length 100, making an acute angle with the positive x-axis. Let the ordinate of P be positive and M be the point on the line segment PQ such that PM:MQ=3:1. Then which of the following points does NOT lie on the line passing through M and perpendicular to the line PQ?

Choose an option

Show full solutionCorrect option: D
Correct answer
D-3,43

Step-by-step explanation

We have been given the length of focal chord PQ=100.

 

Length of focal chord at t=at+1t2=100

Where a=9

t+1t=±103

∴t=3,13,-3,-13

Since ordinate of P is +ve

∴t=3 or 13

(t=3 as slope of PQ is positive)

∴M(21,9)

Required line:y-9=-8060(x-21)

⇒4x+3y=111

-3,43 does not lie on line.

Hence this is the correct option.

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About this question

This is a previous-year question from JEE Main 2023, 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.