MarcLeclair Group Title Convert the following parametric equ'n into a cartesaion equ'n x= squrt (t+1) y=t-2 , So I don't know how to "eliminate" the t. one year ago one year ago

1. SithsAndGiggles Group Title

$\begin{cases}x=\sqrt{t+1}\\y=t-2\end{cases}$ There are two ways to eliminate the $$t$$ here; solve for $$t$$ in terms of $$y$$ and plug it into the first equation, or solve for $$t$$ in terms of $$x$$ and plug it into the second equation. Either way works.

2. MarcLeclair Group Title

So its literally like a system of equation? I was taught with equations including cos and sin, so I was using the unit circle to eliminate t.

3. SithsAndGiggles Group Title

Kind of. The unit circle thing only works for some parametric equations. Let's try the second route: $x=\sqrt{t+1}~~\Rightarrow~~x^2=t+1~~\Rightarrow~t=x^2-1$ Plugging this into the second equation, you get $y=(x^2-1)-2=x^2-3$

4. SithsAndGiggles Group Title

For simple problems like this one, substitution is the way to go.

5. MarcLeclair Group Title

Alright, its weird , this is for Cal 3 and it feels like it's linear algebra/ grade 11 stuff. Anyway thanks!

6. SithsAndGiggles Group Title

You're welcome!