# How do you write the standard equation of a circle with the given radius and center: r=4; C(3,-4)?

May 17, 2018

See below

#### Explanation:

If you know the center $\left({x}_{0} , {y}_{0}\right)$ and the radius $r$ of a circle, you can write its equation as

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

${\left(x - 3\right)}^{2} + {\left(y + 4\right)}^{2} = 16$

you can expand it into

${x}^{2} - 6 x + 9 + {y}^{2} + 8 y + 16 = 16$

and simplify/rearrange into

${x}^{2} + {y}^{2} - 6 x + 8 y + 9 = 0$

Not sure which one you refer to as "standard form", so I hope that one of these calculations fell into it