Find the Center, Vertices, and Foci of the Ellipse with the Given

question 12

Multiple Choice

Find the center, vertices, and foci of the ellipse with the given equation.
- $$\frac { ( x + 5 ) ^ { 2 } } { 100 } + \frac { ( y - 1 ) ^ { 2 } } { 64 } = 1$$

• A) Center: \(( - 5,1 )\); Vertices: \(( 1 , - 15 ) , ( 1,5 ) ;\) Foci: \(( 1 , - 11 ) , ( 1,1 )\)
• B) Center: \(( - 5,1 )\); Vertices: \(( 1 , - 15 ) , ( 1,5 )\); Foci: \(( 1 , - 13 ) , ( 1,3 )\)
• C) Center: \(( - 5,1 )\); Vertices: \(( - 15,1 ) , ( 5,1 )\); Foci: \(( - 13,1 ) , ( 3,1 )\)
• D) Center: \(( - 5,1 )\); Vertices: \(( - 15,1 ) , ( 5,1 )\); Foci: \(( - 11,1 ) , ( 1,1 )\)

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Definitions:

Budget Constraint

A limit on the consumption possibilities of an individual or entity based on available resources.

Optimal Consumption

Describes the combination of goods and services that maximizes an individual's utility or satisfaction subject to their budget constraint.

Marginal Utility

The additional satisfaction or benefit gained from consuming or using one more unit of a good or service.

Deserted Island

An uninhabited or sparsely populated island often used in economic theories and thought experiments to illustrate principles of survival, scarcity, and choice.