Convert the Equation to the Standard Form for a Hyperbola $$4 x ^ { 2 } - 16 y ^ { 2 } - 16 x - 32 y - 64 = 0$$

question 4

Multiple Choice

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
- $$4 x ^ { 2 } - 16 y ^ { 2 } - 16 x - 32 y - 64 = 0$$

• A) \(\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1\)
• B) \(\frac { ( x + 2 ) ^ { 2 } } { 16 } - \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1\)
• C) \(\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1\)
• D) \(\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1\)

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Definitions:

Jung's Personality Theory

A psychological framework positing that the human psyche is made up of the ego, personal unconscious, and collective unconscious, along with archetypes.

Archetypes

Universally recognized symbols, themes, or characters that recur across cultures and literature, often embodying fundamental human experiences.

Unconscious Parts

Elements of the mind that are not within conscious awareness but influence judgments, feelings, or behavior.

Hypervigilance

An enhanced state of sensory sensitivity accompanied by an exaggerated intensity of behaviors whose purpose is to detect threats.