# What is the center and radius of the circle with equation (x - 6)^2 + y^2 = 49?

Jun 3, 2016

Center: $\left(6 , 0\right)$
Radius: $7$

#### Explanation:

A circle centered at $\left({x}_{0} , {y}_{0}\right)$ with radius $r$ has the equation

${\left(x - {x}_{0}\right)}^{2} + {\left(y - {y}_{0}\right)}^{2} = {r}^{2}$

We can make the given equation fit this form with some slight changes:

${\left(x - 6\right)}^{2} + {y}^{2} = 49$

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

Thus the circle is centered at $\left(6 , 0\right)$ and has radius $7$