# How do you write the equation for a circle with center (-2,-3) and r = 3?

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

#### Explanation:

The equation of a circle is:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ where h and k are the x and y values of the centre and r is the radius. We can plug in the given values to find the equation of this circle:

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

May 28, 2016

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

#### 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 = -2 , b = -3 and r = 3

Substitute these values into the standard equation.

$\Rightarrow {\left(x + 2\right)}^{2} + {\left(y + 3\right)}^{2} = 9 \text{ is the circle's equation.}$