Graph the Hyperbola $x ^ { 2 } - y ^ { 2 } - 2 x + 4 y - 19 = 0$

Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. $x ^ { 2 } - y ^ { 2 } - 2 x + 4 y - 19 = 0$

A) center: $( - 1 , - 2 )$ ; vertices: $( - 5 , - 2 ) , ( 3 , - 2 )$ ;
Foci: $( - 1 \pm 4 \sqrt { 2 } , - 2 )$ ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: $\sqrt { 2 }$ ;
Asymptotes: $y = - x - 3 , y = x - 1$ .
B)
Center: $( - 1 , - 2 )$ ;
Vertices: $( - 1 , - 6 ) , ( - 1,2 )$ ;
Foci: $( - 1 , - 2 \pm 4 \sqrt { 2 } )$ ;
length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: $\sqrt { 2 }$ ;
Asymptotes: $y = - x - 3 , y = x - 1$ .
C) center: $( 1,2 )$ ; vertices: $( 1 , - 2 ) , ( 1,6 )$ ;
Foci: $( 1,2 \pm 4 \sqrt { 2 } )$ ;
Length of transverse axis: 4;
Length of conjugate axis: 4;
Eccentricity: $2$ ;
Asymptotes: $y = - x + 3 , y = x + 1$ .
D) center: $( 1,2 )$ ; vertices: $( 1 , - 2 ) , ( 1,6 )$ ;
Foci: $( 1,2 \pm 4 \sqrt { 2 } )$ ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: $\sqrt { 2 }$ ;
Asymptotes: $y = - x + 3 , y = x + 1$ .
E) center: $( 1,2 )$ ; vertices: $( - 3,2 ) , ( 5,2 )$ ;
Foci: $( 1 \pm 4 \sqrt { 2 } , 2 )$ ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: $\sqrt { 2 }$ ;
Asymptotes: $y = - x + 3 , y = x + 1$ .