# How do you find the center and radius for (x - 9)^2 + (y + 11)^2 = 16?

May 28, 2018

$\text{centre "=(9,-11)," radius } = 4$

#### Explanation:

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

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

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

${\left(x - 9\right)}^{2} + {\left(y + 11\right)}^{2} = 16 \text{ is in standard form}$

$\text{with "(a,b)=(9,-(-11))" and } r = \sqrt{16}$

$\text{centre "=(9,11)" and radius } = 4$