Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = —12× + 24

Move the variable to the left-hand side and change its sign Use the commutative property to reorder the terms Factor out $3$ from the expression To complete the square, the same value needs to be added to both sides To complete the square ${x}^{2}+4x+4={\left( x+2 \right)}^{2}$ add $4$ to the expression Since $3 \times 4$ was added to the left-hand side, also add $3 \times 4$ to the right-hand side Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression Simplify the expression Factor out $3$ from the expression To complete the square, the same value needs to be added to both sides To complete the square ${y}^{2}-2y+1={\left( y-1 \right)}^{2}$ add $1$ to the expression Since $3 \times 1$ was added to the left-hand side, also add $3 \times 1$ to the right-hand side Use ${a}^{2}-2ab+{b}^{2}={\left( a-b \right)}^{2}$ to factor the expression Simplify the expression Divide both sides of the equation by $3$ The equation can be written in the form ${\left( x-p \right)}^{2}+{\left( y-q \right)}^{2}={r}^{2}$, so it represents a circle with the radius $r=\sqrt{ 13 }$ and the center $\left( -2, 1\right)$