Find the Standard Form of the Equation of the Hyperbola $( \pm 4,0 )$

question 13

Multiple Choice

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: $( \pm 4,0 )$ ;foci: $( \pm 8,0 )$ ​

• A) \(\frac { y ^ { 2 } } { 48 } - \frac { x ^ { 2 } } { 16 } = 1\)
• B) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 48 } = 1\)
• C) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1\)
• D) \(\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 48 } = 1\)
• E) \(\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1\)

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Definitions:

Extraversion

A characteristic of being sociable, energetic, and having a liking for engaging with others.

Behavioral Traits

Observable and measurable behaviors that are often consistent and unique to an individual.

Personality

The combination of characteristics or qualities that form an individual's distinctive character, influencing patterns of thought, emotion, and behavior.

Consistent

Showing steady conformity to a standard, pattern, or expectation without significant variation.