Circles

Equation of a Circle

let $(x, y)$ be any point on the circle
let $(x_{1}, y_{1})$ be the centre of the circle

\begin{aligned} r & = \sqrt{(x - x_{1})^{2} + (y - y_{1})^{2}} \end{aligned}

\begin{aligned} r & = \sqrt{(x - 0)^{2} + (y - 0)^{2}} \\ r & = \sqrt{x^{2} + y^{2}} \\ r^{2} & = x^{2} + y^{2} \end{aligned}