Write an Equation for the Hyperbola $( 1 , - 2 )$

question 216

Multiple Choice

Write an equation for the hyperbola.
-vertices at $( 1 , - 2 )$ and $( 9 , - 2 )$ , passing through the point $( - 5,16 )$

• A) \(\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 544 } { 7 } } = 1\)
• B) \(\frac { ( x - 5 ) ^ { 2 } } { \frac { 544 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1\)
• C) \(\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 432 } { 7 } } = 1\)
• D) \(\frac { ( x - 5 ) ^ { 2 } } { \frac { 432 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1\)

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Definitions:

Self-serving Bias

A common tendency for individuals to attribute positive outcomes to their own character but attribute negative outcomes to external factors.

Narcissism

A personality trait characterized by an inflated sense of self-importance, need for admiration, and lack of empathy for others.

Learned Helplessness

A scenario where a person is burdened with feelings of inability to exert control, typically following a harrowing event or successive failures.

Confidence

The feeling of self-assurance arising from one's appreciation of one's own abilities or qualities.