# What is the equation of a circle with center (-3, -5) and radius 4?

Mar 7, 2016

${\left(x + 3\right)}^{2} + {\left(y + 5\right)}^{2} = 16$

#### Explanation:

A general circle with centre $\left(a , b\right)$ and radius $r$ has equation ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$.

So in this particular case the equation is

${\left(x + 3\right)}^{2} + {\left(y + 5\right)}^{2} = 16$

Mar 7, 2016

${x}^{2} + {y}^{2} + 6 x + 10 y + 9 = 0$

#### Explanation:

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
$a = - 3 \text{ "b=-5" } r = 4$
${\left(x + 3\right)}^{2} + {\left(y + 5\right)}^{2} = {4}^{2}$
${\left(x + 3\right)}^{2} + {\left(y + 5\right)}^{2} = 16$
${x}^{2} + 6 x + 9 + {y}^{2} + 10 y + 25 = 16$
${x}^{2} + {y}^{2} + 6 x + 10 y + 9 = 0$