Use the Discriminant to Classify the Graph; Then Use the Quadratic

question 90

Multiple Choice

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ .
$$3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } + 10 \sqrt { 3 } x - 6 y - 24 = 0$$

• A) ellipse; \(y = 3 + \sqrt { 3 } x \pm \sqrt { 4 \sqrt { 3 } x + 33 }\)
• B) ellipse; \(y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• C) parabola; \(y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• D) parabola; \(y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• E) hyperbola; \(y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)

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Definitions:

Delayed Hypersensitivity

A type of immune response that occurs days after exposure to an antigen, involving T cells rather than antibodies.

Eosinophils

A type of white blood cell involved in the body's immune response, particularly related to allergies and infections.

Basophils

A type of white blood cell involved in inflammatory responses and allergic reactions.

Monocytes

A type of white blood cell, part of the human body's immune system, that helps to fight off infections by ingesting bacteria, dead cells, and other debris.