# How do you find the equation of the circle given center at the (10, 5) and a radius of 11?

Mar 20, 2018

${\left(x - 10\right)}^{2} + {\left(y - 5\right)}^{2} = 121$

#### Explanation:

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

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

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

$\text{here "(a,b)=(10,5)" and } r = 11$

$\Rightarrow {\left(x - 10\right)}^{2} + {\left(y - 5\right)}^{2} = 121 \leftarrow \textcolor{red}{\text{equation of circle}}$

Mar 20, 2018

${x}^{2} + {y}^{2} - 20 x - 10 y - 4 = 0$

#### Explanation:

To find the equation of a circle whose radius and center has been given, we have a formula,
${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$
where, $h$ and $k$ are the x-coordinate and y-coordinate of the center and $r$ is the radius. So,
${\left(x - 10\right)}^{2} + {\left(y - 5\right)}^{2} = {11}^{2}$
${x}^{2} - 20 x + 100 + {y}^{2} - 10 y + 25 = 121$
${x}^{2} + {y}^{2} - 20 x - 10 y - 4 = 0$

Hope this helps :)