Use the Discriminant to Determine If the Graph of the Equation

question 54

Essay

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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Definitions:

Folliculitis

An inflammation of the hair follicles, often caused by infection, chemical irritation, or physical injury, leading to red, inflamed skin, and, sometimes, pus-filled bumps.

Psoriasis

A chronic skin condition characterized by red, itchy, and scaly patches.

Eczema

A medical condition that makes the skin red, itchy, and inflamed, often chronic and triggered by various factors.

Apocrine Sweat Glands

Glands located in certain areas of the body, such as the armpits, that secrete a thicker sweat and are involved in scent creation.