Graph the Hyperbola $3 y ^ { 2 } - 7 x ^ { 2 } = 1$

Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. $3 y ^ { 2 } - 7 x ^ { 2 } = 1$

A) vertices: $\left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right)$ ;
Foci: $\left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right)$ ;
Length of transverse axis: $\frac { 2 \sqrt { 3 } } { 3 }$ ;
Length of conjugate axis: $\frac { 2 \sqrt { 7 } } { 7 }$ ;
Eccentricity: $\frac { \sqrt { 70 } } { 7 }$ ;
Asymptotes: $y = \pm \frac { \sqrt { 21 } } { 3 } x$ .
B) vertices: $\left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right)$ ;
Foci: $\left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right)$ ;
Length of transverse axis: $\frac { \sqrt { 3 } } { 3 }$ ;
Length of conjugate axis: $2$ ;
Eccentricity: $2$ ;
Asymptotes: $y = \pm \frac { \sqrt { 3 } } { 3 } x$ .
C)
vertices: $\left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right)$ ;
Foci: $\left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right)$ ;
Length of transverse axis: $\frac { 2 \sqrt { 3 } } { 3 }$ ;
Length of conjugate axis: $\frac { 2 \sqrt { 7 } } { 7 }$ ;
Eccentricity: $\frac { \sqrt { 70 } } { 7 }$ ;
Asymptotes: $y = \pm \frac { \sqrt { 21 } } { 7 } x$ .
D) vertices: $\left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right)$ ;
Foci: $\left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right)$ ;
Length of transverse axis: $\frac { 2 \sqrt { 7 } } { 7 }$ ;
Length of conjugate axis: $\frac { 2 \sqrt { 3 } } { 3 }$ ;
Eccentricity: $\frac { \sqrt { 70 } } { 7 }$ ;
Asymptotes: $y = \pm \frac { \sqrt { 21 } } { 7 } x$ .
E) vertices: $\left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right)$ ;
Foci: $\left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right)$ ;
length of transverse axis: $\frac { 2 \sqrt { 3 } } { 3 }$ ;
Length of conjugate axis: $\frac { 2 \sqrt { 7 } } { 7 }$ ;
Eccentricity: $\frac { \sqrt { 70 } } { 7 }$ ;
Asymptotes: $y = \pm \frac { \sqrt { 21 } } { 3 } x$ .