Find the Standard-Form Equation of the Hyperbola Centered at the Origin

question 36

Multiple Choice

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at (2, 0) and (-2, 0) ; foci at (4, 0) and (-4, 0)

• A) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1\)
• B) \(\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1\)
• C) \(\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1\)
• D) \(\frac { x ^ { 2 } } { 12 } - \frac { y ^ { 2 } } { 4 } = 1\)

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Definitions:

Break-Even Sales

The amount of revenue required to cover both the variable and fixed costs of a business, resulting in neither profit nor loss.

Margin Of Safety

The difference between actual sales and sales at the break-even point, providing a cushion that measures the business's ability to withstand sales fluctuations.

Current Sales

The total revenue generated from goods or services sold by a company during the current period.

Break-Even Sales

The amount of revenue required to cover both the fixed and variable costs of a business, indicating the point at which profit starts to be generated.