# What is the equation of the circle with a center at (2 ,2 ) and a radius of 4 ?

Jun 7, 2018

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

#### Explanation:

Formula for a circle centered on $\left(h , k\right)$:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

${\left(x - 2\right)}^{2} + {\left(y - 2\right)}^{2} = {4}^{2}$

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

graph{(x-2)^2 + (y-2)^2 = 16 [-6.67, 13.33, -3.08, 6.92]}

Jun 7, 2018

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

#### Explanation:

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

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

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

$\text{here "(a,b)=(2,2)} \mathmr{and} r = 4$

${\left(x - 2\right)}^{2} + {\left(y - 2\right)}^{2} = 16 \leftarrow \textcolor{red}{\text{equation of circle}}$