# How do you identify the center and the radius of a circle with the equation (x + 5)^2 + (y + 3)^2 = 49?

Jan 19, 2016

centre = ( - 5 , - 3 ) and radius = 7

#### 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 coordinates of the centre and r is radius.

compare ${\left(x + 5\right)}^{2} + {\left(y + 3\right)}^{2} = 49$ with standard form

a = -5 and b = - 3 hence centre = ( - 5 , - 3 )

and ${r}^{2} = 49 \Rightarrow r = \sqrt{49} = 7$