# What is the standard form of the equation of a circle with with the centre (-2,3) and radius 6?

${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = 36$
The equation for a circle is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$, where $\left(h , k\right)$ is the center of the circle and $r$ is the radius.
This translates into: ${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = 36$
Common mistakes when writing the equation are not remembering to flip the signs of $h$ and $k$. Notice that the center is $\left(- 2 , 3\right)$, but the circle's equation has the terms $\left(x + 2\right)$ and $\left(y - 3\right)$. Also, don't forget to square the radius.