What you are describing is a circular motion profile. It is point to point trigonometric function. Without going through all the math, the easy way to generate this is to just use a motion controller, could be a software controller like Mach3 or a hardware controller like a Galil Motion Control product. Both of these have all the hard work done for you. This is a common function of any CNC machine.
Unless you intend to make a 3D arc, like a hemisphere, I'm not sure where the C axis comes into play. But in any case the C axis position would normally be tangent to the X/Y position. If the plot is only in the X/Y plane, then you would only need to describe the points along the arc by the angle (Ø), radius (r), X = r cos Ø, and Y = r sin Ø to do this manually would be rather tedious, that is where the software comes into play. The more points described the smoother the arc plot would be.
Maybe a bit more information would be helpful. What are you using to drive the plotter?