Is it possible to transform a standard equation into parametric form? I know it can be done the other way around, but I am curious if it is possible to split it into two. If so, how can it be done? Thank you.

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Ah, this would be because of the definition of a unit circle. I will do one more. What about x^3+2x^2=y^3 . What would be a good way to go about putting this in a parametric equation.
I am interesting in learning this so I can see how to differentiate standard equations to parametric.

@Dacota Sprague
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Yes, that's it. If the equation has an implicit form, and the other variable can't be isolated, you're forced to use an iterative technique (like Newton Raphson) anyway, so hand analysis is out the window

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## Comments

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TopNewestCan you give an example of an equation that you want to transform?

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Sure. I will provide a relatively simple one... if there is a formula, I wish to understand why. x^2+y^2=25

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One way to express this is:

$x = 5 \, \cos(t) \\ y = 5 \, \sin(t)$

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Ah, this would be because of the definition of a unit circle. I will do one more. What about x^3+2x^2=y^3 . What would be a good way to go about putting this in a parametric equation. I am interesting in learning this so I can see how to differentiate standard equations to parametric.

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I don't think it is useful to do such a transformation for this case, but here is an arbitrary one:

$x = t^{1/2} \\ y = (t^{3/2} + 2t)^{1/3}$

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How were you able to arrive to that conclusion? That is what I'm mainly curious about

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I just chose an expression for x at random. Then I plugged it into your equation and isolated y.

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But that (isolating y) won't always be possible right??? What then???

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So what you are saying is that the parameters for x can be absolutely anything, as long as the other variables stay consistent with those parameters?

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Hmm, so if the parameters can be anything you want, is there any value in finding the derivative of the parameters?? :/

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Yes, there is. In vector calculus, the standard hand-analysis approach for doing line integrals involves differentiating a parametric form

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Actually, I think it is the calculation of the length of a curve that uses it

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