Find the Standard Form of the Equation of the Hyperbola $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = - 1$

question 30

Multiple Choice

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±5) ;focies: (0,±6)
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• A) \(\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = - 1\)
• B) \(\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = 1\)
• C) \(\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = 1\)
• D) \(\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1\)
• E) \(- \frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1\)

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Definitions:

Tail Risk

The risk of an investment moving more than three standard deviations from its current price, often associated with unpredictable, extreme events.

Worst-case Scenario

The most adverse or unfavorable outcome among a set of possibilities for a situation.

Lower Partial Standard Deviation

A risk measure focusing only on negative deviations from the mean, used to assess the downside risk of an investment.

Extreme Negative Returns

Significant losses in investment value over a short period, often unexpected.