Question

The co-ordinate of a moving point $P(a{t}^2,2at)$ where $t$ is a parameter, then find the locus of the point $P$.

Answer 1

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

Let the co-ordinate of the point $P$ be $(x,y)$.

Then $x=a{t}^2$......(1) and $y=2at$ or $t=\frac{y}{2a}$.

Putting the value of $y$ in (1) we get,

$x=a\frac{y^2}{4a^2}$

or, $y^2=4ax$.

This is the locus of the point $P$.