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

question 26

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$$

• A) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0 , - 1 )\) and \(( 8 , - 1 )\)
• foci at \(( 4 - \sqrt { 41 } , - 1 )\) and \(( 4 + \sqrt { 41 } , - 1 )\)
• asymptotes of \(y + 1 = - \frac { 5 } { 4 } ( x - 4 )\) and \(y + 1 = \frac { 5 } { 4 } ( x - 4 )\)
• B) center at \(( - 1,4 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 6,4 )\) and \(( 4,4 )\)
• foci at \(( - 1 - \sqrt { 41 } , 4 )\) and \(( - 1 + \sqrt { 41 } , 4 )\)
• asymptotes of \(y - 4 = - \frac { 4 } { 5 } ( x + 1 )\) and \(y - 4 = \frac { 4 } { 5 } ( x + 1 )\)
• C) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( 4 , - 6 )\) and \(( 4,4 )\)
• foci at \(( 4 , - 1 - \sqrt { 41 } )\) and \(( 4 , - 1 + \sqrt { 41 } )\)
• asymptotes of \(y - 1 = - \frac { 5 } { 4 } ( x + 4 )\) and \(y - 1 = \frac { 5 } { 4 } ( x + 4 )\)
• D) center at \(( 4 , - 1 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 1 , - 1 )\) and \(( 9 , - 1 )\)
• foci at \(( 4 - \sqrt { 41 } , - 1 )\) and \(( 4 + \sqrt { 41 } , - 1 )\)
• asymptotes of \(y + 1 = - \frac { 4 } { 5 } ( x - 4 )\) and \(y + 1 = \frac { 4 } { 5 } ( x - 4 )\)

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