Question

Find the locus of the moving point $P(a{t}^2,2at)$ for $t$ being a parameter.

Answer 1

Given the co-ordinate of the moving point $P$ is $(a{t}^2,2at)$.

Let, $x=a{t}^2\dots \left(1\right)$

$y=2at\dots \left(2\right)$

or, $t=\left(\frac{y}{2a}\right)$

Using this value of $\left(t\right)$ is $\left(1\right)$ we get,

$x=a.y^2/4a^2$

or, $y^2=\left(4ax\right)$.

This is the required locus of $P$.