# How do you find the equation of a circle if the centre of the circle is (5,13) and touches the x axis?

Feb 4, 2016

${\left(x - 5\right)}^{2} + {\left(y - 13\right)}^{2} = {13}^{2}$

#### Explanation:

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

If the center of the center of a circle is at $\left(\textcolor{red}{5} , \textcolor{b l u e}{13}\right)$ and it is tangent to the X-axis
then its radius is the distance from the center to the X-axis,
i.e. the $y$ coordinate of its center (in this case $\textcolor{g r e e n}{13}$)