Find an Equation in Standard Form for the Ellipse That $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$

question 70

Multiple Choice

Find an equation in standard form for the ellipse that satisfies the given conditions.
-The vertical major axis is of length 8 , and the minor axis is of length 4 .

• A) \(\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1\)
• B) \(\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 4 } = 1\)
• C) \(\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 2 } = 1\)
• D) \(\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1\)

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Definitions:

Indifference Curves

A graphical representation showing combinations of two goods that give a consumer equal satisfaction and utility, reflecting preferences.

Perfect Substitutes

Goods or services that can be used in exactly the same way, such that the consumer is indifferent between one and another.

Perfect Complements

Goods that are consumed together in fixed proportions, where the use of one item increases the value or necessity of the other.

Indifference Curves

Graphical representations in microeconomics showing combinations of two goods among which a consumer is indifferent, indicating equal utility.