# How do you find the center and radius of the circle x^2 −2x + y^2 − 6y = 26?

May 1, 2016

Center is $\left(1 , 3\right)$ and radius is $6$

#### Explanation:

General equation of a circle is of the form

${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0$, whose center is $\left(- g , - f\right)$ and radius is $\sqrt{{g}^{2} + {f}^{2} - c}$

Hence in the equation of circle ${x}^{2} - 2 x + {y}^{2} - 6 y = 26$ is of the form

${x}^{2} + {y}^{2} - 2 x - 6 y - 26 = 0$ and hence

$g = - 1$, $f = - 3$ and $c = - 26$

Hence, center of circle is $\left(- \left(- 1\right) , - \left(- 3\right)\right)$ or $\left(1 , 3\right)$

and radius is $\sqrt{{\left(- 1\right)}^{2} + {\left(- 3\right)}^{2} - \left(- 26\right)} = \sqrt{1 + 9 + 26} = \sqrt{36} = 6$

graph{x^2+y^2-2x-6y-26=0 [-10, 10, -5, 5]}