Equations of Circle

For a circle $\mathscr{C}$ with centre $(h,k)$ and radius $r$, the equation of $\mathscr{C}$ is
\begin{equation*}
(x-h)^2+(y-k)^2 = r^2.
\end{equation*}

For any circle $\mathscr{C}$, the equation of $\mathscr{C}$ can be rewritten to the form
\begin{equation*}
x^2+y^2+Dx+Ey+F=0,
\end{equation*}
where $D$, $E$ and $F$ are real numbers.

1. Centre $= (\dfrac{-D}{2},\dfrac{-E}{2})$
2. Radius $= \sqrt{\left(\dfrac{D}{2}\right)^2+ \left(\dfrac{E}{2}\right)^2 – F}$