# What are the coordinates of the radius of the circle x^2 + y^2 -8x -10y -8=0?

Feb 5, 2016

The circle has a center i $C = \left(4 , 5\right)$ and radius $r = 7$

#### Explanation:

To find the coordinates of the center and the radius of a circle we have to transform its equation to form of:

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

In the given example we can do this by doing:

${x}^{2} + {y}^{2} - 8 x - 10 y - 8 = 0$

${x}^{2} - 8 x + 16 + {y}^{2} - 10 y + 25 - 8 - 16 - 25 = 0$

${\left(x - 4\right)}^{2} + {\left(y - 5\right)}^{2} - 49 = 0$

Finally:

${\left(x - 4\right)}^{2} + {\left(y - 5\right)}^{2} = 49$

From this equation we get the center and the radius.