Let $O$ be the vertex, $Q$ be any point on the parabola $x^2=8 y$. If the point $P$ divides the line segment $O Q$ internally in the ratio $1: 3$, then the locus of $P$ is

Question

Let $O$ be the vertex, $Q$ be any point on the parabola $x^2=8 y$. If the point $P$ divides the line segment $O Q$ internally in the ratio $1: 3$, then the locus of $P$ is, $x^2=y$, $y^2=x$, $y^2=2 x$, $x^2=2 y$

MARKS App · Accepted Answer

Hint : $\begin{aligned} & O P: P Q=1: 3 \ & \Rightarrow \mathrm{h}=\mathrm{t}, \mathrm{k}=\frac{\mathrm{t}^2}{2} \ & \Rightarrow \mathrm{k}=\frac{\mathrm{h}^2}{2}\end{aligned}$

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