Find an Equation for the Ellipse Described $( - 4,5 )$

question 165

Multiple Choice

Find an equation for the ellipse described.
-Vertices at $( - 4,5 )$ and $( 16,5 )$ ; focus at $( 14,5 )$

• A) \(\frac { ( x + 6 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1\)
• B) \(\frac { ( x - 6 ) ^ { 2 } } { 49 } - \frac { ( y + 2 ) ^ { 2 } } { 19 } = 1\)
• C) \(\frac { ( x - 6 ) ^ { 2 } } { 100 } + \frac { ( y - 5 ) ^ { 2 } } { 36 } = 1\)
• D) \(\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 6 ) ^ { 2 } } { 15 } = 1\)

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Definitions:

Risk-neutral

A risk preference situation where an individual or entity does not prefer risk but also does not avoid it, valuing potential gains and losses equally.

Risk-averse

A characteristic of preferring to avoid loss over making a gain, typically by selecting the option with the smallest possible risk.

Expected Utility

A theory in economics that quantifies how choices are made when the outcomes are uncertain.

Utility

A measure of satisfaction or pleasure that individuals get from the consumption of goods and services.