NIMCET 2023 — Mathematics PYQ

Let $M$ be the mid-point of VP is $(h,k)$
$h=\frac{0+a{t}^2}{2}\Rightarrow a{t}^2=2h$
$k=\frac{0+2at}{2}\Rightarrow at=k\Rightarrow t=\frac{k}{a}$
Put value of $t$ in Eq. (i), we get
$k^2=2ah$
Replace $h\to x$ and $k\to y$
$y^2=2ax$
Put $a=1$
Now, we get
$y^2=2x$