Use the Discriminant to Determine If the Graph of the Equation

question 7

Essay

Use the discriminant to determine if the graph of the equation $13 x ^ { 2 } - 10 x y + 13 y ^ { 2 } - 72 = 0$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.