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.

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Definitions:

Tracheal Tubes

A system of branching air ducts within insects that spread across the body to facilitate the exchange of gases.

Body Surface

The outermost layer or covering of an organism's body, including the skin, fur, or scales, which serves as a protective barrier.

Nudibranch Mollusks

Colorful sea slugs found in marine environments, known for their striking forms and colors.

Tracheal Tubes

The system of small tubes in insects and some other arthropods that carry air directly to tissues from openings in the exoskeleton.