First slide

Parabola

Question

The locus of a point which divides the line segment joining the point $(0, - 1)$ and a point on the parabola $x^{2} = 4 y$ internally in the ratio 1:2 is:

Easy

A

$4 x^{2} - 3 y = 2$
B

$x^{2} - 3 y = 2$
C

$9 x^{2} - 3 y = 2$
D

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

Solution

Let P(0, -1) , $Q (2 t, t^{2})$ and R (h, k)
Given that R divides PQ in 1:2,
$∴ h = \frac{2 t}{3}, k = \frac{- 2 + t^{2}}{3}$
Hence locus is $3 k + 2 = {(\frac{3 h}{2})}^{2} \Rightarrow 9 x^{2} = 12 y + 8$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App