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

question 45

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $25 y ^ { 2 } - 16 x ^ { 2 } = 400$

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