# What is the standard form of the equation of a circle with a center (7, 3) and a diameter of 24?

Nov 29, 2015

${\left(x - 7\right)}^{2} + {\left(y - 3\right)}^{2} = 144$

#### Explanation:

The standard form of a circle centered at $\left({x}_{1} , {y}_{1}\right)$ with radius $r$ is
${\left(x - {x}_{1}\right)}^{2} + {\left(y - {y}_{1}\right)}^{2} = {r}^{2}$

The diameter of a circle is twice its radius. Therefore a circle with diameter $24$ will have radius $12$. As ${12}^{2} = 144$, centering the circle at $\left(7 , 3\right)$ gives us

${\left(x - 7\right)}^{2} + {\left(y - 3\right)}^{2} = 144$