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:
Correct Option: 1
Solution:
Let point $P$ be $\left(2 t, t^{2}\right)$ and $Q$ be $(h, k)$
Using section formula,
$h=\frac{2 t}{3}, k=\frac{-2+t^{2}}{3}$
Hence, locus is $3 k+2=\left(\frac{3 h}{2}\right)^{2}$
$\Rightarrow \quad 9 x^{2}=12 y+8$
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