# How do you find an equation of the sphere with center (1, −9, 3) and radius 5?

Mar 15, 2017

See explanation.

#### Explanation:

The standard equation of a sphere with radius $r$ and center in $S = \left(a , b , c\right)$ is:

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} + {\left(z - c\right)}^{2} = {r}^{2}$

So in the given example it turns to:

${\left(x - 1\right)}^{2} + {\left(y + 9\right)}^{2} + {\left(z - 3\right)}^{2} = 25$