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

question 47

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $x ^ { 2 } - 16 y ^ { 2 } - 8 x - 64 y - 64 = 0$

• A) center at \(( - 2,4 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 6,4 )\) and \(( 2,4 )\)
• foci at \(( - 2 - \sqrt { 17 } , 4 )\) and \(( - 2 + \sqrt { 17 } , 4 )\)
• asymptotes of \(y - 4 = - \frac { 1 } { 4 } ( x + 2 )\) and \(y - 4 = \frac { 1 } { 4 } ( x + 2 )\)
• B) center at \(( 4 , - 2 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0 , - 2 )\) and \(( 8 , - 2 )\)
• foci at \(( 4 - \sqrt { 17 } , - 2 )\) and \(( 4 + \sqrt { 17 } , - 2 )\)
• asymptotes of \(y + 2 = - \frac { 1 } { 4 } ( x - 4 )\) and \(y + 2 = \frac { 1 } { 4 } ( x - 4 )\)
• C) center at \(( 4 , - 2 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 3 , - 2 )\) and \(( 5 , - 2 )\)
• foci at \(( 4 - \sqrt { 17 } , - 2 )\) and \(( 4 + \sqrt { 17 } , - 2 )\)
• asymptotes of \(y + 2 = - 4 ( x - 4 )\) and \(y + 2 = 4 ( x - 4 )\)
• D) center at \(( 4 , - 2 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( 4 , - 6 )\) and \(( 4,2 )\)
• foci at \(( 4 , - 2 - \sqrt { 17 } )\) and \(( 4 , - 2 + \sqrt { 17 } )\)
• asymptotes of \(y - 2 = - 4 ( x + 4 )\) and \(y - 2 = 4 ( x + 4 )\)

---

Definitions:

Germ Line

The sequence of reproductive cells that can give rise to gametes, ensuring genetic continuity from generation to generation.

Morphogenesis

The biological process that causes an organism to develop its shape, usually beginning in the early stages of embryonic development.

Recognizable Structures

Physical formations or arrangements within an organism or system that can be distinctly identified and are often associated with specific functions or processes.

Pattern Formation

Refers to the process through which cells undergo spatial organization during embryonic development to form structured tissues and organs.