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EXAMPLE 3: x 2  y 2  2gx  2 fy  c  0

Find the centre and the length of the
Center , C = ( - g , - f )

radius of the circle x  y  6x  12y   2 2
2
2
2 0
Solution : Radius , r  g  f  c

By comparing the equation to the general form


x  y  2gx  2 fy c  0
2
2

We find 2g   6 and 2 f  12

g   3 and f  6


 g 

, f 

 3, 6
so we obtain the centre at and
r  g  f  c
2
2

2
2
r  ( ) 3  6  ( ) 2

r  47