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

##### 1 Answer

Jan 29, 2016

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

#### Explanation:

The general form of the equation of a circle is :

# x^2 + y^2 + 2gx + 2fy + c = 0 # given equation is :

#x^2 + y^2 + 18x - 12y - 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+(-6)^2 +27 ) = 12 #