# How do you find the center and radius of the circle given (x+3)^2+(y+7)^2=81?

Oct 5, 2016

$\text{The centre : (-3,-7) and radius } r = 9.$

#### Explanation:

Recall that the eqn. of a circle having centre at $\left(h , k\right) \text{ & radius } r$ is :

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2.} \ldots \ldots \ldots \ldots \ldots \ldots \left(\star\right)$.

Comparing the given eqn. with $\left(\star\right)$, we immediately find that

the centre is $\left(- 3 , - 7\right)$ and radus $r = 9.$