Use the Discriminant to Classify the Graph; Then Use the Quadratic

Multiple Choice

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ .
$$3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 0$$

A) ellipse; $\quad y = - 15 + \sqrt { 3 } x \pm \sqrt { 12 \sqrt { 3 } x + 189 }$
B) ellipse; $y = - 15 + \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }$
C) parabola; $y = - 15 + \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }$
D) parabola; $y = \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }$
E) hyperbola; $y = \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }$