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.
- $$( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9$$

A) center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices: $( 4 , - 5 )$ and $( 4,1 )$
foci: $( 4 , - 2 - \sqrt { 10 } )$ and $( 4 , - 2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$
B) center: $( - 4,2 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices: $( - 4 , - 1 )$ and $( - 4,5 )$
foci: $( - 4,2 - \sqrt { 10 } )$ and $( - 4,2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$
C) center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices: $( 5 , - 4 )$ and $( 5,2 )$
foci: $( 5 , - 1 - \sqrt { 10 } )$ and $( 5 , - 1 + \sqrt { 10 } )$
asymptotes of $y + 2 = - \frac { 1 } { 3 } ( x - 4 )$ and $y + 2 = \frac { 1 } { 3 } ( x - 4 )$
D) center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { x }$ -axis
vertices: $( - 4 , - 3 )$ and $( 4,3 )$
foci: $( 4 , - \sqrt { 10 } )$ and $( 4 , \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$