Answer
$y=\pm x^{3/2}$, or
$ y^{2}=x^{3}, \quad x \geq 0,\ \ t\in \mathbb{R}, \ \ y\in \mathbb{R}$
See image:
Work Step by Step
Build a table of coordinates (x,y)
$x=f(t)=t^{2},\quad \qquad y=g(t)=t^{3}$
Plot the points and join with a smooth curve.
Taking the initial t to be the first point in the table, track the direction in which the points "travel" as t increases.
b.
From $ x=t^{2},\ \ \quad x \geq 0,\ \ t\in \mathbb{R}, \ \ t=\pm\sqrt{x}$
Substituting t into the other equation, we get
$y=t^{3}$
$y=\pm x^{3/2}$, or
$y^{2}=x^{3}$
