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 $y = \frac { 1 } { 2 } x$

Question

Quizplus · Accepted Answer

The equation of the hyperbola can be rewritten as $\frac{x^2}{4^2} - \frac{y^2}{2^2} = 1$, indicating a center at (0,0), a transverse axis along the x-axis, vertices at $(-4,0)$ and $(4,0)$, foci at $(-2\sqrt{5}, 0)$ and $(2\sqrt{5}, 0)$, and asymptotes of $y = \pm \frac{1}{2}x$.

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