# How do you find the center and radius for x^2 + (y + 6)^2 = 49 ?

Sep 10, 2016

centre = (0 ,-6) , radius = 7

#### 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.

${x}^{2} + {\left(y + 6\right)}^{2} = 49 \text{ is in this form.}$

That is ${\left(x - 0\right)}^{2} + {\left(y - \left(- 6\right)\right)}^{2} = {7}^{2}$

and by comparison with the standard form.

$a = 0 , b = - 6 \text{ and } r = 7$

Thus, centre = (0 ,-6) and radius = 7