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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$x ^ { 2 } - 16 y ^ { 2 } + 6 x - 32 y - 23 = 0$$

A) center at $( - 3 , - 1 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 7 , - 1 )$ and $( 1 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $y + 1 = - \frac { 1 } { 4 } ( x + 3 )$ and $y + 1 = \frac { 1 } { 4 } ( x + 3 )$

B) center at $( - 3 , - 1 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices at $( - 3 , - 5 )$ and $( - 3,3 )$
foci at $( - 3 , - 1 - \sqrt { 17 } )$ and $( - 3 , - 1 + \sqrt { 17 } )$
asymptotes of $\mathrm { y } - 1 = - 4 ( \mathrm { x } - 3 )$ and $\mathrm { y } - 1 = 4 ( \mathrm { x } - 3 )$

C) center at $( - 3 , - 1 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 4 , - 1 )$ and $( - 2 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $\mathrm { y } + 1 = - 4 ( \mathrm { x } + 3 )$ and $\mathrm { y } + 1 = 4 ( \mathrm { x } + 3 )$

D) center at $( - 1 , - 3 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 5 , - 3 )$ and $( 3 , - 3 )$
foci at $( - 1 - \sqrt { 17 } , - 3 )$ and $( - 1 + \sqrt { 17 } , - 3 )$
asymptotes of $y + 3 = - \frac { 1 } { 4 } ( x + 1 )$ and $y + 3 = \frac { 1 } { 4 } ( x + 1 )$

Correct Answer:

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