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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9$$

A) center at $( 3 , - 3 )$
transverse axis is parallel to $\mathrm { y }$ -axis
vertices at $( 3 , - 6 )$ and $( 3,0 )$ ,
foci at $( 3 , - 3 - \sqrt { 10 } )$ and $( 3 , - 3 + \sqrt { 10 } )$ ,
asymptotes of $y - 3 = - 3 ( x + 3 )$ and $y - 3 = 3 ( x + 3 )$

B) center at $( 3 , - 3 )$
transverse axis is parallel to $x$ -axis
vertices at $( 0 , - 3 )$ and $( 6 , - 3 )$
foci at $( 3 - \sqrt { 10 } , - 3 )$ and $( 3 + \sqrt { 10 } , - 3 )$
asymptotes of $y + 3 = - \frac { 1 } { 3 } ( x - 3 )$ and $y + 3 = \frac { 1 } { 3 } ( x - 3 )$

C) center at $( - 3,3 )$
transverse axis is parallel to $x$ -axis
vertices at $( - 6,3 )$ and $( 0,3 )$
foci at $( - 3 - \sqrt { 10 } , 3 )$ and $( - 3 + \sqrt { 10 } , 3 )$
asymptotes of $y - 3 = - \frac { 1 } { 3 } ( x + 3 )$ and $y - 3 = \frac { 1 } { 3 } ( x + 3 )$

D) center at $( 3 , - 3 )$
transverse axis is parallel to $x$ -axis
vertices at $( 2 , - 3 )$ and $( 4 , - 3 )$
foci at $( 3 - \sqrt { 10 } , - 3 )$ and $( 3 + \sqrt { 10 } , - 3 )$
asymptotes of $y + 3 = - 3 ( x - 3 )$ and $y + 3 = 3 ( x - 3 )$

Correct Answer:

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