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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.

  • 11 months ago
  • 11 months ago

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

    • 11 months ago
  2. MarcLeclair Group Title
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    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.

    • 11 months ago
  3. SithsAndGiggles Group Title
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    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 \[y=(x^2-1)-2=x^2-3\]

    • 11 months ago
  4. SithsAndGiggles Group Title
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    For simple problems like this one, substitution is the way to go.

    • 11 months ago
  5. MarcLeclair Group Title
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    Alright, its weird , this is for Cal 3 and it feels like it's linear algebra/ grade 11 stuff. Anyway thanks!

    • 11 months ago
  6. SithsAndGiggles Group Title
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    You're welcome!

    • 11 months ago
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