# How do you find an equation of the circle with center (2,4) and radius 3?

Dec 6, 2015

${x}^{2} + {y}^{2} - 4 x - 8 y = - 11$

#### Explanation:

If you know the coordinates of the center to be $\left({x}_{0} , {y}_{0}\right)$ and the radius to be $r$, then the equation of the circle with these center and radius is

${\left(x - {x}_{0}\right)}^{2} + {\left(y - {y}_{0}\right)}^{2} = {r}^{2}$.

Plug your values and you have

${\left(x - 2\right)}^{2} + \left(y - 4\right) = 9$

You can either leave the equation as it is, or expand it:

${x}^{2} - 4 x + 4 + {y}^{2} - 8 y + 16 = 9$

${x}^{2} + {y}^{2} - 4 x - 8 y = - 11$