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JEE Main 201511 AprilOnline

Exam: JEE Main
Year: 2015
Date: 11 April
Mode: Online
Subject: Mathematics
Chapter: Parabola

JEE Main 2015 · 11 April · Online · Mathematics · Parabola

If PQ be a double ordinate of the parabola, y ^ 2 = - 4x, where P...

If

PQ

be a double ordinate of the parabola,

{y}^{2} = - 4x,

where

P

lies in the second quadrant. If

R

divides

PQ

in the ratio

2: 1,

then the locus of

R

is:

If PQ be a double ordinate of the parabola, y ^ 2 = - 4x, where P lies in the second quadrant. If R divides PQ in the

Options

A $3{y}^{2} = - 2x$
B $9{y}^{2} = 4x$
C $9{y}^{2} = - 4x$
D $3{y}^{2} = 2x$

Correct answer

C. $9{y}^{2} = - 4x$

Step-by-step solution

If PQ be a double ordinate of the parabola, y ^ 2 = - 4x, where P lies in the second quadrant. If R divides PQ in the

Let $P\left(- {t}^{2}, 2t\right) \text{\text{ and } } Q\left(- {t}^{2}, - 2t\right)$

$R$ divides in the ratio $2: 1$

\left(\dfrac{- 2{t}^{2} - {t}^{2}}{2 + 1}, \dfrac{- 4t + 2t}{2 + 1}\right) $</p><p>\left(- {t}^{2}, \dfrac{2}{3}t\right)$

$x = - {t}^{2}$

$y = - \dfrac{2}{3}t$

$∴ 9{y}^{2} = 4{t}^{2}$

$⇒ 9{y}^{2} = - 4x$

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