How do you write an equation of a circle whose center (-1, 2) and radius 4?

May 15, 2016

${\left(x + 1\right)}^{2} + {\left(y - 2\right)}^{2} = 16$

Explanation:

The general equation of a circle with center $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ and radius $\textcolor{g r e e n}{r}$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \textcolor{red}{a}\right)}^{2} + {\left(y - \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{g r e e n}{r}}^{2}$

Given $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right) = \left(\textcolor{red}{- 1} , \textcolor{b l u e}{2}\right)$
and $\textcolor{g r e e n}{r} = \textcolor{g r e e n}{4}$
this becomes
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \left(\textcolor{red}{- 1}\right)\right)}^{2} + {\left(y - \textcolor{b l u e}{2}\right)}^{2} = {4}^{2}$

which would normally be simplified as
$\textcolor{w h i t e}{\text{XXX}} {\left(x + 1\right)}^{2} + {\left(y - 2\right)}^{2} = 16$