# Parametrizing a curve

1. Jan 15, 2013

### cytochrome

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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?

2. Jan 16, 2013

### CAF123

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

3. Jan 16, 2013

### cytochrome

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. Jan 16, 2013

### LCKurtz

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.