# What is the equation of a circle with radius 9 and center (-2,3)?

The equation of a circle with its center at point $\left(a , b\right)$ with radius $c$ is given by ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {c}^{2}$. In this case, therefore, the equation of the circle is ${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = {9}^{2}$.
The explanation above is enough detail, I think, as long as the signs $\left(+ \mathmr{and} -\right)$ of the points are carefully noted.