# How do you write the equation for a circle with center at (-5, 6) and diameter = 16?

May 11, 2016

${\left(x + 5\right)}^{2} + {\left(y - 6\right)}^{2} = 64$

#### Explanation:

The general equation for a circle with center $\left(a , b\right)$ and radius $r$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

We are told the center $\left(a , b\right) = \left(- 5 , 6\right)$
and that the diameter $= 16$
which implies the radius is $r = 8$

So we have
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \left(- 5\right)\right)}^{2} + {\left(y - 6\right)}^{2} = {8}^{2}$
or
$\textcolor{w h i t e}{\text{XXX}} {\left(x + 5\right)}^{2} + {\left(y - 6\right)}^{2} = 64$

Here is the graph for ${\left(x + 5\right)}^{2} + {\left(y - 6\right)}^{2} = 64$
graph{(x+5)^2+(y-6)^2=64 [-20.35, 15.68, -3.46, 14.56]}