# How do you write the equation of the circle where the point (-6,-5) lies on a circle whose center is at (-4,5)?

Apr 11, 2016

$\textcolor{red}{{\left(x + 4\right)}^{2} + {\left(y - 5\right)}^{2} = 104}$

#### Explanation:

$r = \sqrt{{\overline{A O}}^{2} + {\overline{A B}}^{2}}$
$r = \sqrt{{\left(- 6 + 4\right)}^{2} + {\left(- 5 - 5\right)}^{2}}$

$r = \sqrt{{\left(- 2\right)}^{2} + {\left(- 10\right)}^{2}}$

$r = \sqrt{4 + 100}$

$r = \sqrt{104}$

${r}^{2} = 104$

$O = \left(a , b\right) \text{ circle's center}$
$O = \left(- 4 , 5\right)$
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2} \text{ circle equation}$

$\textcolor{red}{{\left(x + 4\right)}^{2} + {\left(y - 5\right)}^{2} = 104}$