Find an Equation for the Hyperbola Described $( 0 , - 8 )$

question 90

Multiple Choice

Find an equation for the hyperbola described.
-Vertices at $( 0 , - 8 )$ and $( 0,8 ) ;$ asymptote the line $y = \frac { 4 } { 9 } x$

• A) \(\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 81 } = 1\)
• B) \(\frac { y ^ { 2 } } { 81 } - \frac { x ^ { 2 } } { 16 } = 1\)
• C) \(\frac { y ^ { 2 } } { 324 } - \frac { x ^ { 2 } } { 64 } = 1\)
• D) \(\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 324 } = 1\)

---

Definitions:

Environmental Factor

denotes any non-genetic influence, ranging from climate to culture, which can affect living organisms and their development.

Bipolar II Disorder

Mood disorder characterized by alternating periods of extremely depressed and mildly elevated moods.

Major Depressive Disorder

A mental disorder characterized by a persistent feeling of sadness and loss of interest, affecting daily functioning.

Cognitive Triad

A psychological theory that identifies an individual's beliefs about themselves, their world, and their future as key elements in understanding depression.