# How do you write the equation of a circle with a center at (4, 1) and a radius of 6?

Apr 30, 2018

${\left(x - 4\right)}^{2} + {\left(y - 1\right)}^{2} = 36$

#### Explanation:

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

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

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

$\text{here "(a,b)=(4,1)" and } r = 6$

$\Rightarrow {\left(x - 4\right)}^{2} + {\left(y - 1\right)}^{2} = 36 \leftarrow \textcolor{b l u e}{\text{equation of circle}}$