Question

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.

Answer 1

\[\begin{cases}x=\sqrt{t+1}\\y=t-2\end{cases}\]
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.

Answer 2

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.

Answer 3

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
\[y=(x^2-1)-2=x^2-3\]

Answer 4

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

Answer 5

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

Answer 6

You're welcome!