# What are the coordinates of the center and the length of the radius of the circle represented by the equation x^2+y^2-4x+8y+11=0?

Jun 2, 2017

Center C=(2;-4), radius $r = 3$

#### Explanation:

To find the radius and center we have to transform the equation to

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

${x}^{2} + {y}^{2} - 4 x + 8 y + 11 = 0$

${x}^{2} - 4 x + 4 - 4 + {y}^{2} + 8 y + 16 - 16 + 11 = 0$

${\left(x - 2\right)}^{2} - 4 + {\left(y + 4\right)}^{2} - 16 + 11 = 0$

${\left(x - 2\right)}^{2} + {\left(y + 4\right)}^{2} - 9 = 0$

${\left(x - 2\right)}^{2} + {\left(y + 4\right)}^{2} = 9$

From the transformed equation we can see that the circle's center is C=(2;-4) and radius $r = 3$