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 \(y - 2 = 4 ( x + 4 )\)

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