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

question 8

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9$$

• A) center: \(( 4 , - 2 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices: \(( 4 , - 5 )\) and \(( 4,1 )\)
• foci: \(( 4 , - 2 - \sqrt { 10 } )\) and \(( 4 , - 2 + \sqrt { 10 } )\)
• asymptotes of \(y + 2 = - 3 ( x - 4 )\) and \(y + 2 = 3 ( x - 4 )\)
• B) center: \(( - 4,2 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices: \(( - 4 , - 1 )\) and \(( - 4,5 )\)
• foci: \(( - 4,2 - \sqrt { 10 } )\) and \(( - 4,2 + \sqrt { 10 } )\)
• asymptotes of \(y + 2 = - 3 ( x - 4 )\) and \(y + 2 = 3 ( x - 4 )\)
• C) center: \(( 4 , - 2 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices: \(( 5 , - 4 )\) and \(( 5,2 )\)
• foci: \(( 5 , - 1 - \sqrt { 10 } )\) and \(( 5 , - 1 + \sqrt { 10 } )\)
• asymptotes of \(y + 2 = - \frac { 1 } { 3 } ( x - 4 )\) and \(y + 2 = \frac { 1 } { 3 } ( x - 4 )\)
• D) center: \(( 4 , - 2 )\)
• transverse axis is parallel to \(\mathrm { x }\)-axis
• vertices: \(( - 4 , - 3 )\) and \(( 4,3 )\)
• foci: \(( 4 , - \sqrt { 10 } )\) and \(( 4 , \sqrt { 10 } )\)
• asymptotes of \(y + 2 = - 3 ( x - 4 )\) and \(y + 2 = 3 ( x - 4 )\)

---

Definitions:

Skilled Labor

Workforce with specialized knowledge, training, and experience requiring advanced skills and education.

Unskilled Labor

Work that requires no specialized skills, education, or training, and often involves manual labor.

Unemployment Insurance

A government-provided financial assistance program for individuals who have lost their jobs, offering temporary financial support.

Monetary Transfer

The process of moving money from one entity to another, often as a method of payment, financial support, or in the form of aid.