Finding the speed of a point moving around a circle

[imsoconfused]

Homework Statement

Find x(t), y(t) so that the point goes around the circle (x-1)^2 + (y-3)^2 = 4 with speed 1.

Homework Equations

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

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.

 

[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?

 

[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?

 

[Defennder]

Have you learned 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

 

[imsoconfused]

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

 

[imsoconfused]

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

 

[Defennder]

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