Use the discriminant to determine if the graph of the equation, $16 x ^ { 2 } - 24 x y + 9 y ^ { 2 } - 60 x - 80 y = 0$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.

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The Answer of Use the discriminant to determine if the graph of the equation, $16 x ^ { 2 } - 24 x y + 9 y ^ { 2 } - 60 x - 80 y = 0$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.

Use the Discriminant to Determine If the Graph of the Equation