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.
- $$\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$$

A) center at $( 4 , - 1 )$
transverse axis is parallel to $x$ -axis
vertices at $( 0 , - 1 )$ and $( 8 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 5 } { 4 } ( x - 4 )$ and $y + 1 = \frac { 5 } { 4 } ( x - 4 )$

B) center at $( - 1,4 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 6,4 )$ and $( 4,4 )$
foci at $( - 1 - \sqrt { 41 } , 4 )$ and $( - 1 + \sqrt { 41 } , 4 )$
asymptotes of $y - 4 = - \frac { 4 } { 5 } ( x + 1 )$ and $y - 4 = \frac { 4 } { 5 } ( x + 1 )$

C) center at $( 4 , - 1 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices at $( 4 , - 6 )$ and $( 4,4 )$
foci at $( 4 , - 1 - \sqrt { 41 } )$ and $( 4 , - 1 + \sqrt { 41 } )$
asymptotes of $y - 1 = - \frac { 5 } { 4 } ( x + 4 )$ and $y - 1 = \frac { 5 } { 4 } ( x + 4 )$

D) center at $( 4 , - 1 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 1 , - 1 )$ and $( 9 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 4 } { 5 } ( x - 4 )$ and $y + 1 = \frac { 4 } { 5 } ( x - 4 )$