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

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 $\mathrm{y}$ -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 $y=-\frac{4}{5}$ and $y=\frac{4}{5}$