Identify the Foci and Write Equations for the Asymptotes $$9 ( y - 4 ) ^ { 2 } - 100 ( x + 4 ) ^ { 2 } = - 900$$

question 32

Multiple Choice

Identify the foci and write equations for the asymptotes.
- $$9 ( y - 4 ) ^ { 2 } - 100 ( x + 4 ) ^ { 2 } = - 900$$

• A) foci: \(( - 4 + \sqrt { 109 } , 4 ) , ( - 4 - \sqrt { 109 } , 4 )\)
• asymptotes: \(y = \frac { 10 } { 3 } x + \frac { 52 } { 3 }\) and \(y = \frac { 10 } { 3 } x - \frac { 28 } { 3 }\)
• B) foci: \(( 0 , - 4 + \sqrt { 109 } ) , ( 0 , - 4 - \sqrt { 109 } )\)
• asymptotes: \(y = \frac { 3 } { 10 } x - \frac { 14 } { 5 }\) and \(y = - \frac { 3 } { 10 } x - \frac { 26 } { 5 }\)
• C) foci: \(( 4 + \sqrt { 109 } , 0 ) , ( 4 - \sqrt { 109 } , 0 )\)
• asymptotes: \(y = \frac { 10 } { 3 } x - \frac { 28 } { 3 }\) and \(y = \frac { 10 } { 3 } x + \frac { 52 } { 3 }\)
• D) foci: \(( 0,4 + \sqrt { 109 } ) , ( 0,4 - \sqrt { 109 } )\)
• asymptotes: \(y = \frac { 3 } { 10 } x + \frac { 26 } { 5 }\) and \(y = - \frac { 3 } { 10 } x + \frac { 14 } { 5 }\)

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Consumer Surplus

The difference between what consumers are willing to pay and what they actually pay.

Market Price

The current price at which a good or service can be bought or sold, determined by the forces of supply and demand.

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A loss of economic efficiency that can occur when the free market equilibrium for a good or a service is not achieved.

Under Production

A situation where less is produced than could be achieved with the available resources, often leading to inefficiencies and unmet demand.