# How do you write the equation of the circle with center point (2,4) and passing through point (4,-1)?

Jun 22, 2016

${\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 29$

#### Explanation:

The radius of the circle is
$\textcolor{w h i t e}{\text{XXX}} r = \sqrt{{\left(2 - 4\right)}^{2} + {\left(- 1 - 4\right)}^{2}} = \sqrt{29}$

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

In this case
$\textcolor{w h i t e}{\text{XXX}} {\left(x - 2\right)}^{2} + {\left(y - 4\right)}^{2} = 29$