Question

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

Answer 1

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`