The general polar equation of a circle of radius [math]ρ[/math] centered at [math](r_0;θ_0)[/math]is [br][br][math]r^2-2rr_0\cos\left(\theta-\theta_0\right)+r_0^2=\rho[/math].[br]This equation is derived from the Law of Cosines.[br][br]Using that [math]r=\sqrt{x^2+y^2}[/math] and [math]\tan\left(\theta\right)=\frac{y}{x}[/math] we can transform this polar equation to a cartesian one:[br][br]

Instead of the [math]\arctan[/math] we use [i]atan2(y,x)[/i] in GeoGebra, as this function gives us an angle in [0,360)

Another possibility is to use the general circle equation in cartesian form[br][math]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/math] and substitute [math]h=r_0\cos\left(\theta_0\right)[/math] and [math]k=r_0\sin\left(\theta_0\right)[/math] so we get[br][br][math]\left(x-r_0\cos\left(\theta_0\right)\right)^2+\left(y-r_0\sin\left(\theta_0\right)\right)^2=\rho^2[/math] as the implicit equation.