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

question 37

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { ( x + 4 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$$

• A) center at \(( - 4 , - 3 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 10 , - 3 )\) and \(( 2 , - 3 )\)
• foci at \(( - 4 - 2 \sqrt { 13 } , - 3 )\) and \(( - 4 + 2 \sqrt { 13 } , - 3 )\)
• asymptotes of \(y + 3 = - \frac { 2 } { 3 } ( x + 4 )\) and \(y + 3 = \frac { 2 } { 3 } ( x + 4 )\)
• B) center at \(( - 4 , - 3 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 8 , - 3 )\) and \(( 0 , - 3 )\)
• foci at \(( - 4 - 2 \sqrt { 13 } , - 3 )\) and \(( - 4 + 2 \sqrt { 13 } , - 3 )\)
• asymptotes of \(y + 3 = - \frac { 3 } { 2 } ( x + 4 )\) and \(y + 3 = \frac { 3 } { 2 } ( x + 4 )\)
• C) center at \(( - 3 , - 4 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 7 , - 4 )\) and \(( 1 , - 4 )\)
• foci at \(( - 3 - 2 \sqrt { 13 } , - 4 )\) and \(( - 3 + 2 \sqrt { 13 } , - 4 )\)
• asymptotes of \(y + 4 = - \frac { 3 } { 2 } ( x + 3 )\) and \(y + 4 = \frac { 3 } { 2 } ( x + 3 )\)
• D) center at \(( - 4 , - 3 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( - 4 , - 7 )\) and \(( - 4,1 )\)
• foci at \(( - 4 , - 3 - 2 \sqrt { 13 } )\) and \(( - 4 , - 3 + 2 \sqrt { 13 } )\)
• asymptotes of \(y - 3 = - \frac { 2 } { 3 } ( x - 4 )\) and \(y - 3 = \frac { 2 } { 3 } ( x - 4 )\)

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