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

question 44

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$4 x ^ { 2 } - 16 y ^ { 2 } = 64$$

• A) center at \(( 0,0 )\)
• transverse axis is \(x\)-axis
• vertices: \(( - 2,0 ) , ( 2,0 )\)
• foci: \(( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )\)
• asymptotes of \(y = - \frac { 1 } { 2 } x\) and \(y = \frac { 1 } { 2 } x\)
• B) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { x }\)-axis
• vertices: \(( 0 , - 4 ) , ( 0,4 )\)
• foci: \(( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )\)
• asymptotes of \(y = - \frac { 1 } { 2 } x\) and \(y = \frac { 1 } { 2 } x\)
• C) center at \(( 0,0 )\)
• transverse axis is \(x\)-axis
• vertices: \(( - 4,0 ) , ( 4,0 )\)
• foci: \(( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )\)
• asymptotes of \(y = - \frac { 1 } { 2 } x\) and \(y = \frac { 1 } { 2 } x\)
• D) center at \(( 0,0 )\)
• transverse axis is \(x\)-axis
• vertices: \(( - 4,0 ) , ( 4,0 )\)
• foci: \(( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )\)
• asymptotes of \(y = - \frac { 1 } { 2 } x\) and \(y = \frac { 1 } { 2 } x\)