# How do you write the equation of a circle with a center at (7, 3) and a diameter of 24?

Jan 20, 2016

${\left(x - 7\right)}^{2} + {\left(y - 3\right)}^{2} = {12}^{2}$

#### Explanation:

If the diameter is $24$ then the radius is $r = \frac{24}{2} = 12$

The general formula for a circle with center $\left(a , b\right)$ and radius $r$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

Substituting the given values for $\left(a , b\right)$ and the calculated value for $r$ gives
$\textcolor{w h i t e}{\text{XXX}} {\left(x - 7\right)}^{2} + {\left(y - 3\right)}^{2} = {12}^{2}$

Personally I think the equation should be left in this form. (it provides the maximum amount of information).

However if you need it "expanded":
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 14 x + 49 + {y}^{2} - 6 y + 9 = 144$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + {y}^{2} - 14 x - 6 y = 86$