Parametrizing a curve

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Homework Statement



Find a vector-valued function f that parametrizes the curve (x-1)^2 + y^2 = 1


Homework Equations



(x-1)^2 + y^2 = 1


The Attempt at a Solution



The equation is the graph of a circle that is 1 unit to the right of the origin, therefore a parametrization would be

x(t) = cos(t) + 1
y(t) = sin(t)

Therefore a vector-valued function that parametrizes this curve is given by

r(t) = (cos(t) + 1)i + sin(t)j


I've been having trouble with parametrization lately so I was wondering if this is correct. Also, is there a better method to go about this sort of thing? Is it entirely visual and you just have to have a "feel" for it?
 

Answers and Replies

  • #2
CAF123
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Yes, that would be a correct parametrisation. There are of course ways to check that it is correct.
 
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Yes, that would be a correct parametrisation. There are of course ways to check that it is correct.

But is there an algorithm or anything to go about it? I just had to visualize it. Will every parametrization problem be like that?
 
  • #4
LCKurtz
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But is there an algorithm or anything to go about it? I just had to visualize it. Will every parametrization problem be like that?

I would say pretty much yes to that. There are always many possible parameterizations and often some are more natural or "better" than others for a particular purpose. In your example, visualizing it as a circle and thinking in terms of sines and cosines is exactly the appropriate approach. There isn't a magic procedure that will always mindlessly work.
 

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