Find the Center, Transverse Axis, Vertices, Foci, and Asymptotes of the Hyperbola

question 1

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$$

• A) center at \(( 0,0 )\)
• transverse axis is \(x\)-axis
• vertices at \(( - 11,0 )\) and \(( 11,0 )\)
• foci at \(( - \sqrt { 137 } , 0 )\) and \(( \sqrt { 137 } , 0 )\)
• asymptotes of \(y = - \frac { 11 } { 4 }\) and \(y = \frac { 11 } { 4 }\)
• B) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { y }\)-axis
• vertices at \(( 0 , - 4 )\) and \(( 0,4 )\)
• foci at \(( - \sqrt { 137 } , 0 )\) and \(( \sqrt { 137 } , 0 )\)
• asymptotes of \(y = - \frac { 11 } { 4 }\) and \(y = \frac { 11 } { 4 }\)
• C) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { x }\)-axis
• vertices at \(( - 4,0 )\) and \(( 4,0 )\)
• foci at \(( - 11,0 )\) and \(( 11,0 )\)
• asymptotes of \(y = - \frac { 11 } { 4 }\) and \(y = \frac { 11 } { 4 }\)
• D) center at \(( 0,0 )\)
• transverse axis is \(x\)-axis
• vertices at \(( - 4,0 )\) and \(( 4,0 )\)
• foci at \(( - \sqrt { 137 } , 0 )\) and \(( \sqrt { 137 } , 0 )\)
• asymptotes of \(y = - \frac { 11 } { 4 }\) and \(y = \frac { 11 } { 4 }\)

---

Definitions:

Fixed Asset

Long-term tangible property that a company owns and uses in its operations to generate income, such as buildings, machinery, and equipment, which are not expected to be consumed or converted into cash within a year.

Property, Plant, Equipment

Long-term assets held for business use and not intended for resale, such as buildings, machinery, and vehicles, subject to depreciation.

Depreciated

A decrease in the value of an asset over time due to wear and tear or obsolescence.

Operating Efficiency

A measure of how effectively a company uses its resources to generate profits.