R^2/Circle/Circumference/Definition

Circle

Let ${}M=(a,b)\in \mathbb {R} ^{2}$ and ${}r\in \mathbb {R} _{+}$. Then the set

${\left\{(x,y)\in \mathbb {R} ^{2}\mid (x-a)^{2}+(y-b)^{2}=r^{2}\right\}}$

is called the circle with center ${}M$ and radius ${}r$.