Find an Equation in Standard Form for the Hyperbola That $( 0 , \pm 10 )$

question 74

Multiple Choice

Find an equation in standard form for the hyperbola that satisfies the given conditions.
-Foci at $( 0 , \pm 10 )$ , a conjugate axis with length 8

• A) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1\)
• B) \(\frac { y ^ { 2 } } { 84 } - \frac { x ^ { 2 } } { 16 } = 1\)
• C) \(\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 64 } = 1\)
• D) \(\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 100 } = 1\)

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Definitions:

Midrange

Theories or concepts that operate at an intermediate level of abstraction, bridging the gap between grand theories and specific empirical instances, often in the context of social sciences.

Self-fulfilling Prophecy

A phenomenon where an initially inaccurate expectation leads to actions that cause the expectation to come true, thereby confirming its own accuracy.

Outcome Expectancy

An individual's belief about the likelihood that a specific behavior or action will lead to a particular outcome.

Optimistic Bias

The tendency to believe that one is less likely to experience negative events and more likely to experience positive events compared to others.