Find the Standard-Form Equation of the Hyperbola Centered at the Origin

question 303

Multiple Choice

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at $( 0,4 )$ and $( 0 , - 4 )$ ; asymptotes $y = \frac { 2 } { 3 } x$ and $y = - \frac { 2 } { 3 } x$

• A) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 36 } = 1\)
• B) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1\)
• C) \(\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 16 } = 1\)
• D) \(\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1\)

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Definitions:

Eysenck's Factors

A personality model proposing three dimensions of human personality: extraversion-introversion, neuroticism-stability, and psychoticism-superego.

Psychoticism

A personality pattern typified by aggressiveness and interpersonal hostility, related to the liability to have psychotic thinking or experiences.

Agreeableness

A personality trait characterized by attributes such as trust, altruism, kindness, affection, and other prosocial behaviors.

Conscientiousness

A personality trait characterized by diligence, carefulness, thoroughness, and organization.