# How do you write the equation of the circle with radius 9 and center (-2,3)?

Aug 3, 2016

${\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = 81$

#### Explanation:

The equation of a circle in standard form is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where (a ,b) are the coordinates of the centre and r, the radius.

here a = -2 , b = 3 and r = 9

substitute these values into the standard equation.

${\left(x - \left(- 2\right)\right)}^{2} + {\left(y - 3\right)}^{2} = {9}^{2}$

$\Rightarrow {\left(x + 2\right)}^{2} + {\left(y - 3\right)}^{2} = 81 \text{ is the equation of the circle}$