` 3x ^(2) + 3y ^(2) + 12x - 18y - 11 = 0 `
` rArr x ^(2) + y ^(2) + 4x - 6y - (11)/(3) = 0" "`... (i)
This is of the form ` x ^(2) + y ^(2) + 2 gx + 2 fy +c = 0`,
`" " ` where ` 2g = 4, 2 f = - 6 and c = - (11)/(3)`
` therefore g = 2, f =- 3 and c = - (11)/(3)`
Hence, the given equation represents a circle.
Centre of the circle ` = (-g, - f ) = (-2, 3)`
Radius of the circle `= sqrt(g ^(2) + f ^(2) - c ) `
`" " =sqrt ((-2) ^(2) + 3 ^(2) + (11)/(3)) = sqrt (( 50 )/(3)) ` units
