Find the centre and the radius of the equation 3x²+ 3y²+ 6x -4y -1 =0 of the circle.

first of all divide the whole eq. by 3 

as we know the eq. of the cirle is = x²+y²+2gx +2fy +c = 0......1

so the eq, will become = x²+y²+2x - (4/3) y -(1/3)= 0 ........2

comparing 1 &2

2g = 2 .......g= 1

2f = - 4/3 ......f= -2/3

& c = -1/3

so , centre of circle = C( -g , -f) = C( -1, 2/3 )

& radius = whole  sq. root of  g²+f²--C

= whole sq root of  1²+(2/3)² - (-1/3)

=sq. root of (16/9) = 4/3

therefore r = 4/3 & C( -1, (2/3) )