Circle as an implicit equation in polar form
The general polar equation of a circle of radius centered at is
.
This equation is derived from the Law of Cosines.
Using that and we can transform this polar equation to a cartesian one:
Instead of the we use atan2(y,x) in GeoGebra, as this function gives us an angle in [0,360)
Another possibility is to use the general circle equation in cartesian form
and substitute and so we get
as the implicit equation.