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 \(y + 2 = 3 ( x - 4 )\)

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