# What is the equation (in standard form) for a circle with center (2,7) and radius 4?

The standard form for the equation of a circle with center $\left(a , b\right)$ and radius $r$ is ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$. In this case, the equation of the circle is ${\left(x - 2\right)}^{2} + {\left(y - 7\right)}^{2} = 16$
The common tricks are to note the minus signs in the standard form, and to remember that the expression in the standard form is for ${r}^{2}$ so the radius itself is the square root of that expression.