# How do you find the equation of the circle given center:(0,0) radius: 2 square root of 7?

Oct 16, 2016

The equation of a circle with center $\left(a , b\right)$ and radius $r$ is:

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

#### Explanation:

For this problem $a = 0 , b = 0 , r = 2 \sqrt{7}$

Then the equation is:

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {\left(2 \sqrt{7}\right)}^{2}$, that is:

${x}^{2} + {y}^{2} = 4 \cdot 7$

So the equation is: ${x}^{2} + {y}^{2} = 28$