anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\begin{cases}x=\sqrt{t+1}\\y=t-2\end{cases}\] 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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
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 \[y=(x^2-1)-2=x^2-3\]

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anonymous
  • anonymous
For simple problems like this one, substitution is the way to go.
anonymous
  • anonymous
Alright, its weird , this is for Cal 3 and it feels like it's linear algebra/ grade 11 stuff. Anyway thanks!
anonymous
  • anonymous
You're welcome!

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