# How do you find an equation of the circle whose center is (-3,1) and whose radius is 8?

May 8, 2018

${\left(x + 3\right)}^{2} + {\left(y - 1\right)}^{2} = 64$

#### Explanation:

$\text{the equation of a circle in standard form is}$

$\textcolor{red}{\overline{\underline{|} \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{2}{2}} |}}$

$\text{where "(a,b)" are the coordinates of the centre and r}$
$\text{is the radius}$

$\text{here "(a,b)=(-3,1)" and } r = 8$

${\left(x - \left(- 3\right)\right)}^{2} + {\left(y - 1\right)}^{2} = {8}^{2}$

$\Rightarrow {\left(x + 3\right)}^{2} + {\left(y - 1\right)}^{2} = 64 \leftarrow \textcolor{red}{\text{equation of circle}}$