Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Q.

Let P be a point on the parabola, $y^{2} = 12 x$ 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 $\frac{4}{3}$ , then

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

a

$P N = 3$

b

$M Q = \frac{1}{4}$

c

$M Q = \frac{1}{3}$

d

$P N = 4$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

detailed_solution_thumbnail

We have, $y^{2} = 12 x$
Let $P (3 t^{2}, 6 t), N (3 t^{2}, 0), M (3 t^{2}, 3 t)$
Question Image

Equation of MQ is $y = 3 t$

$∴ Q = (\frac{3}{4} t^{2}, 3 t)$

Equation of NQ is $y - 0 = \frac{3 t}{(\frac{3}{4} t^{2} - 3 t^{2})} (x - 3 t^{2})$
$\Rightarrow y = \frac{3 t}{3 t^{2} (\frac{- 3}{4})} (x - 3 t^{2}) \Rightarrow y = \frac{- 4}{3 t} x + 4 t$
Given that y-intercept of NQ=4/3
$∴ 4 t = \frac{4}{3} \Rightarrow t = \frac{1}{3} ∴ M Q = 3 t^{2} - \frac{3}{4} t^{2} = \frac{9}{4} t^{2} = \frac{1}{4} a n d P N = 6 t = 2$

Watch 3-min video & get full concept clarity

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Not sure what to do in the future? Don’t worry! We have a FREE career guidance session just for you!

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, then