# Finding the speed of a point moving around a circle

1. Sep 17, 2008

### imsoconfused

1. The problem statement, all variables and given/known data
Find x(t), y(t) so that the point goes around the circle (x-1)^2 + (y-3)^2 = 4 with speed 1.

2. Relevant equations
I know that the center of the circle is (1,3) and that the radius of the circle is 4.

3. The attempt at a solution
Well, I'm really confused by what the author means by "speed". I know it's |v| (v being the velocity), but I still don't get what he is asking for. I know I need to find parametric equations x(t) and y(t) which, when combined, would give the equation of the circle, but I don't know how to work backwards like that. integration?
this shouldn't be this hard, I'm just being retarded, sorry.

2. Sep 17, 2008

### Defennder

You need a parametric vector representation of a circle. The equation of the circle you are given is in Cartesian form, but you want one in terms of parameter t.

Once you have x(t) and y(t). You can then write $$\mathbf{r}(t) = x(t)\mathbf{i} + y(t)\mathbf{j}$$ How would you find |v| from here?

3. Sep 18, 2008

### imsoconfused

yes, once I get it into the parameterized form, I know where to go. however, getting there is another issue--I'm really confused about finding x(t) and y(t). where does t come from?

4. Sep 18, 2008

### Defennder

Have you learnt the parametric representation of a circle? You can check Wikipedia for it. t is just the parameter which varies.

Wikipedia has it as:
x = a + r cos t
y = b + r sin t

5. Sep 18, 2008

### imsoconfused

no, I hadn't. seems like we would have covered that in class! thanks though.

6. Sep 18, 2008

### imsoconfused

are my equations now x = 1 + 4cost, y = 3 + 4sint?

7. Sep 18, 2008

### Defennder

It's supposed to be r cos t and r sin t, where r is the radius.

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