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

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

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