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

question 151

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9$$

• A) center at \(( 3 , - 3 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( 3 , - 6 )\) and \(( 3,0 )\),
• foci at \(( 3 , - 3 - \sqrt { 10 } )\) and \(( 3 , - 3 + \sqrt { 10 } )\),
• asymptotes of \(y - 3 = - 3 ( x + 3 )\) and \(y - 3 = 3 ( x + 3 )\)
• B) center at \(( 3 , - 3 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0 , - 3 )\) and \(( 6 , - 3 )\)
• foci at \(( 3 - \sqrt { 10 } , - 3 )\) and \(( 3 + \sqrt { 10 } , - 3 )\)
• asymptotes of \(y + 3 = - \frac { 1 } { 3 } ( x - 3 )\) and \(y + 3 = \frac { 1 } { 3 } ( x - 3 )\)
• C) center at \(( - 3,3 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 6,3 )\) and \(( 0,3 )\)
• foci at \(( - 3 - \sqrt { 10 } , 3 )\) and \(( - 3 + \sqrt { 10 } , 3 )\)
• asymptotes of \(y - 3 = - \frac { 1 } { 3 } ( x + 3 )\) and \(y - 3 = \frac { 1 } { 3 } ( x + 3 )\)
• D) center at \(( 3 , - 3 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 2 , - 3 )\) and \(( 4 , - 3 )\)
• foci at \(( 3 - \sqrt { 10 } , - 3 )\) and \(( 3 + \sqrt { 10 } , - 3 )\)
• asymptotes of \(y + 3 = - 3 ( x - 3 )\) and \(y + 3 = 3 ( x - 3 )\)

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