Parametric Equations to Cartesian Equation

Question

What is the cartesian equation of the set of parametric equations:

$x=2t^2$

$y=3t^3$

This is my attempt:

$x=2t^2$

$t^2=x/2$

$y=3t^3$

$t^3=y/3$

I do not know how to deal with this from here.

Answer 1

Following what you did, we then have

$$\frac{y}{3}=t^3=(t^2)^{3/2}=\left(\frac{x}{2}\right)^{3/2}$$

Raising both sides to the square, we obtain

$$\frac{y^2}{9}=\frac{x^3}{8}$$

And hence $$8y^2-9x^3=0$$ is the equation you are looking for.