# How do you write an equation for a circle with center(4,7) and passing through (3,-2)?

${\left(x - 4\right)}^{2} + {\left(y - 7\right)}^{2} = 82$

#### Explanation:

Using the center - radius form

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

The radius $r$ may be computed using the center and the given point

$r = \sqrt{{\left(7 - - 2\right)}^{2} + {\left(4 - 3\right)}^{2}}$

$r = \sqrt{82}$

Let us formulate the equation

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

${\left(x - 4\right)}^{2} + {\left(y - 7\right)}^{2} = {\left(\sqrt{82}\right)}^{2}$

${\left(x - 4\right)}^{2} + {\left(y - 7\right)}^{2} = 82$

God bless....I hope the explanation is useful.