# The center of a circle is at (-2, 3) and it has a radius of 3. What is the equation of the circle?

Feb 14, 2016

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

#### Explanation:

Standard Equation of a Circle:
${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

where
$C : \left(h , k\right)$
$r$ = radius

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

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

Feb 14, 2016

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

#### Explanation:

the standard form of the equation of a circle is

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
where (a , b) are the coords of the centre and r , the radius.

here (a , b ) = ( -2 , 3 ) and r = 3
substitute these values into the equation to obtain

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