# How do you write the equation of the circle with center (-1,3) and radius 3?

Oct 8, 2016

${\left(x + 1\right)}^{2} + {\left(y - 3\right)}^{2} = 9$

#### Explanation:

The standard form of the equation of a circle 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 = -1 , b = 3 and r = 3

substitute values into the standard equation.

${\left(x - \left(- 1\right)\right)}^{2} + {\left(y - 3\right)}^{2} = {3}^{2}$

$\Rightarrow {\left(x + 1\right)}^{2} + {\left(y - 3\right)}^{2} = 9 \text{ is the equation of the circle}$