# How do you find the equation of a circle with center at (-6, 2), passing through the point (-3,6)?

Feb 2, 2016

${\left(x + 6\right)}^{2} + {\left(y - 2\right)}^{2} = 25$

#### Explanation:

The line segment from the point $\left(- 6 , 2\right)$ to the point $\left(- 3 , 6\right)$ is a radius of the said circle. We can find the length of the radius using Pythagoras Theorem.

$r = \sqrt{{\left(- 6 - \left(- 3\right)\right)}^{2} + {\left(2 - 6\right)}^{2}}$

$= \sqrt{9 + 16}$
$= 5$

Equation of circle:

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