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MarcLeclair

  • 2 years ago

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.

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  1. SithsAndGiggles
    • 2 years ago
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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.

  2. MarcLeclair
    • 2 years ago
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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.

  3. SithsAndGiggles
    • 2 years ago
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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 \[y=(x^2-1)-2=x^2-3\]

  4. SithsAndGiggles
    • 2 years ago
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    For simple problems like this one, substitution is the way to go.

  5. MarcLeclair
    • 2 years ago
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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!

  6. SithsAndGiggles
    • 2 years ago
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    You're welcome!

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