Use the Discriminant to Determine If the Graph of the Equation

Essay

Use the discriminant to determine if the graph of the equation, $13 x ^ { 2 } + 6 \sqrt { 3 } x y + 7 y ^ { 2 } = 64$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.