# How do you write the equation for a circle with center (2a, a) and touching the y-axis?

Nov 8, 2016

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

#### Explanation:

If the circle touches the Y-axis then the radius of the circle is equal to the horizontal distance from the Y-axis to the center of the circle.

The distance from the Y-axis to the center of the circle is the $x$ coordinate of the center of the circle.

So in this case the radius is $2 a$.

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

So the equation for a circle with cneter $\left(\textcolor{red}{2 a} , \textcolor{b l u e}{a}\right)$ and radius $\textcolor{g r e e n}{2 a}$ is
${\textcolor{w h i t e}{\text{XXX")(x-color(red)(2a))^2+(y-color(blue)a)^2=color(green)(} \left(2 a\right)}}^{2}$