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?

By inspection $ y=x^2$ here.. but it is always not possible in $x$ to be solved for $t$ or a function of $t$ to plug it into $y$ or vice versa. — Narasimham, Jun 10 '18 at 00:03

score 3 · Answer 1 · answered Jun 09 '18 at 17:20

3

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

so $y=x^2$.

answered Jun 09 '18 at 17:20

nonuser

90,026

Ok, thank you but this wasn't exactly the best example as it is easy to see. My bad. The post was edited – Edward B Jun 09 '18 at 17:24
3

You must not do that. Ask another question, don't just edit it. – nonuser Jun 09 '18 at 17:27

How do I eliminate an element from two parametric equations?

1 Answers1