$\displaystyle x= 3t$
$\displaystyle y= 9t^2$
Find the cartesian equation.
I don't get what one is.
The answer is $\displaystyle t^2$.
thanks!
$\displaystyle t^2$ is not a cartesian equation. It's not even an equation..
As far as I know, cartesian equations are equations that describe the curve using x and y coordinates, not parameters like $\displaystyle t$.
$\displaystyle x = 3t$
$\displaystyle y = 9t^2$
You can see that $\displaystyle y = x^2$.
If you can't see the relation between x and y (parametric equations are not always simple like this), you can do it algebraically.
$\displaystyle x = 3t$
$\displaystyle t = \frac{x}{3}$
$\displaystyle y = 9t^2$
$\displaystyle y = 9 (\frac{x}{3})^2$
$\displaystyle y = x^2$