# How do you write the equation for a circle with center of circle (-3,0) radius with endpoint (3,0)?

Aug 27, 2017

${\left(x + 3\right)}^{2} + {y}^{2} = 36$

#### Explanation:

The equation of a circle is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$, where $\left(h , k\right)$ is the center and $r$ is the radius.

If the center is at $\left(- 3 , 0\right)$ and the endpoint of the radius is at $\left(3 , 0\right)$, then the length of the radius is the distance between the two points, which is $3 - \left(- 3\right) = 6$.

We can substitute color(blue)((color(blue)(-3, 0)) for $\left(h , k\right)$, and $\textcolor{red}{6}$ for $r$.

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

${\left(x - \textcolor{b l u e}{\left(- 3\right)}\right)}^{2} + {\left(y - \textcolor{b l u e}{0}\right)}^{2} = {\textcolor{red}{6}}^{2}$

${\left(x + 3\right)}^{2} + {y}^{2} = 36$

We can check this by graphing. The center of the circle is at $\left(- 3 , 0\right)$ and the endpoint of the radius is at $\left(3 , 0\right)$, so our equation is correct.