how do I write equation of a circle in cylindrical coordinates?

Question

assuming the circle is 2 dimensional, only raised up to 3 dimen by a z value.

Answer 1

If the center of the circle is at the point (0,0,z0), and it lies in a plane parallel to the xy-plane, and it has a radius c, then it has a very simple equation: r=c, z=z0.

On the other hand, if the center is at the point (x0,y0,z0), and the polar coordinates of the point (x0,y0) are (r0,theta0), then the equation is

r^2 - 2r*r0*cos(theta-theta0) + r0^2 = c^2, z=z0.