# What is the center and radius of the circle with equation x^2 + y^2 + 18x – 12y – 27 = 0?

Jan 29, 2016

centre = ( - 9 , 6 ) and r = 12

#### Explanation:

The general form of the equation of a circle is :

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

given equation is : ${x}^{2} + {y}^{2} + 18 x - 12 y - 27 = 0$

By comparison : 2g = 18 → g = 9 and 2f = - 12 → f = -6 , c = -27

centre = ( - g , - f ) = (- 9 , 6 )

and r $= \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{9}^{2} + {\left(- 6\right)}^{2} + 27} = 12$