Yeah this makes sense. Sorry for my mistake. You'll only need two variables to plot a 1-d object in a 2d space.
You would need four parameters to specify a shifted circle in either coordinate system. (The k and h parameters will propagate through your transformation.) You could transform this shift into polar coordinates as well (and you would have to if this was a complicated mechanics problem) but you don't even need to bother with this because it is given as a constant.