JEE Main 2021MathematicsStraight LinesEasyMCQ

JEE Main 2021 — Straight Lines Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

Let A be a fixed point (0,6) and B be a moving point (2t,0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is

Choose an option

Show full solutionCorrect option: D
Correct answer
D2x2+3y-9=0

Step-by-step explanation

Mid point M=t,3

mAB=-3t

Perpendicular bisector of AB is 

y-3=t3x-t

So, C=0, 3-t23

Let P be h, k

h=t2; k=3-t26

⇒k=3-4h26

⇒2x2+3y-9=0

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About this question

This is a previous-year question from JEE Main 2021, covering the Straight Lines 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.