Answer
$${\text{circle}}$$
Work Step by Step
$$\eqalign{
& 3{x^2} + 12x + 3{y^2} = 0 \cr
& {\text{Divide by 3}} \cr
& {x^2} + 4x + {y^2} = 0 \cr
& {\text{Complete the square}} \cr
& {x^2} + 4x + 4 + {y^2} = 4 \cr
& {\left( {x + 2} \right)^2} + {y^2} = 4 \cr
& {\text{The equation is in the form }}{\left( {x - h} \right)^2} + {\left( {y - h} \right)^2} = {r^2} \cr
& {\text{Therefore, the equation represents a circle centered at }}\left( { - 2,0} \right) \cr
& {\text{Graph}} \cr} $$
