# How do you find the center and radius for x^2 - 8x + y^2 - 4y – 5 = 0?

Jun 10, 2016

Center is $\left(4 , 2\right)$ and radius is $5$

#### Explanation:

In the equation of a circle in form

${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0$

The center of circle is at $\left(- g , - f\right)$ and radius is $\sqrt{{g}^{2} + {f}^{2} - c}$

In equation ${x}^{2} - 8 x + {y}^{2} - 4 y - 5 = 0$, $g = - 4$, $f = - 2$ and $c = - 5$

Hence, center is $\left(4 , 2\right)$ and radius is

$\sqrt{{4}^{2} + {2}^{2} - \left(- 5\right)} = \sqrt{25} = 5$

graph{x^2-8x+y^2-4y-5=0 [-7.08, 15.42, -3.345, 7.905]}