How do you express the center of a circle in cylindrical coordinates?

[btbam91]

This is something I have zero familiarity with.

Anyways, I was given the equation:

r=2asin(theta)+2bcos(theta) and had to prove that it was a circle, and then state its center in cartesian and cylindrical coordinates. After making the appropriate substitutions and completing the square (twice), I got:

(x-b)^2 + (y-a)^2 = a^2+b^2

Obviously, the center in cartesian coordinates are (b,a).

But how do I express this center in cylindrical coordinates? Thanks!

 

[Mark44]

Cylindrical coordinates are three-dimensional, with the first two coordinates being the same as two-d polar coordinates, r and $\theta$. Use the formulas for converting from cartesian to polar coordinates.