Verified Solution • 2025–26 Session moderate

QJEEM20Ma2377: JEE Main 2020 Mathematics - Class 11 JEEM20Ma2377 Solution: Let P be a point on the parabola, y 2 = 12x and N be the foot…

Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is 43{4 \over 3} , then :

Multiple Choice Options

  • A MQ = 13{1 \over 3}
  • B PN = 4
  • C PN = 3
  • D MQ = 14{1 \over 4}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 3rd September Morning Slot Mathematics - Parabola Question 88 English Explanation

Let P = (3t2 , 6t) ; N = (3t2 , 0)

M = (3t2 , 3t)

Let point Q = (h, 3t) which lies on the parabola y2 = 12x

∴\therefore 9t2 = 12h

⇒\Rightarrow h = 3t24{{3{t^2}} \over 4}

Equation of NQ

y - 0 = 3t3t24−3t2(x−3t2){{3t} \over {{{3{t^2}} \over 4} - 3{t^2}}}\left( {x - 3{t^2}} \right)

⇒\Rightarrow y = −43t(x−3t2){{ - 4} \over {3t}}\left( {x - 3{t^2}} \right)

For y-intercept of NQ, x = 0

∴\therefore y = 4t

Given y-intercept of the line NQ is 43{4 \over 3}

∴\therefore 4t = 43{4 \over 3}

⇒\Rightarrow t = 13{1 \over 3}

∴\therefore MQ = 9t24{{9{t^2}} \over 4} = 14{1 \over 4}

PN = 6t = 2

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring