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JEE Main 20208 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 8 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Parabola

JEE Main 2020 · 8 January · Morning Shift · Mathematics · Parabola

The locus of a point which divides the line segment joining the...

The locus of a point which divides the line segment joining the point

\left(0, - 1\right)

and a point on the parabola

{x}^{2} = 4y

internally in the ratio

1: 2

is:

Options

A $9{x}^{2} - 12y = 8$
B $9{x}^{2} - 3y = 2$
C ${x}^{2} - 3y = 2$
D $4{x}^{2} - 3y = 2$

Correct answer

A. $9{x}^{2} - 12y = 8$

Step-by-step solution

Let point

P

be \left(2t, {t}^{2}\right)

and Q be \left(h, k\right)

.

h = \dfrac{2t}{3}, k = \dfrac{- 2 + {t}^{2}}{3}

Hence, locus is

3k + 2 = {\left(\dfrac{3h}{2}\right)s}^{2} ⇒ 9{x}^{2} = 12y + 8

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