How do I eliminate an element from two parametric equations?

Question

I'm trying to finish some mechanics exercises here but I'm stuck with this, and as I haven't really done math in a while, I can't seem to solve it alone

I have two parametric equations:

M: $x = e^{3t} + t$

$y = e^{6t} +2e^{3t}t + t^{2}$

Basically what I need to do is remove the 't' element and be left with a standalone equation for a trajectory. Any ideas/tips?

Answer 1

Well $$x^2 = (e^{3t}+t)^2 = e^{6t} +2e^{3t}t + t^{2}=y$$

so $y=x^2$.