# How to find the center and radius of 2x^2 + 2y^2 -8x +12y +8=0?

Jan 29, 2016

centre = (2 , -3 ) and r = 3

#### Explanation:

The general equation of a circle is

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

For the given equation to be compared require to divide by 2 .

hence equation is ${x}^{2} + {y}^{2} - 4 x + 6 y + 4 = 0$

Comparing the equation to the general form.

then 2g = - 4 → g = - 2 and 2f = 6 →f = 3 , c=4

centre = ( - g , - f ) = (2 , - 3 )

and r = $\sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{\left(- 2\right)}^{2} + {3}^{2} - 4} = 3$