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) $Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 7 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x . B) vertices: \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ; Foci: \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ; Length of transverse axis: \frac { \sqrt { 3 } } { 3 } ; Length of conjugate axis: 2 ; Eccentricity: 2 ; Asymptotes: y = \pm \frac { \sqrt { 3 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . D) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 7 } } { 7 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x .$ 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) $Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 7 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x . B) vertices: \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ; Foci: \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ; Length of transverse axis: \frac { \sqrt { 3 } } { 3 } ; Length of conjugate axis: 2 ; Eccentricity: 2 ; Asymptotes: y = \pm \frac { \sqrt { 3 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . D) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 7 } } { 7 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x .$ 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) $Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 7 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x . B) vertices: \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ; Foci: \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ; Length of transverse axis: \frac { \sqrt { 3 } } { 3 } ; Length of conjugate axis: 2 ; Eccentricity: 2 ; Asymptotes: y = \pm \frac { \sqrt { 3 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . D) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 7 } } { 7 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x .$
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) $Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 7 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x . B) vertices: \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ; Foci: \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ; Length of transverse axis: \frac { \sqrt { 3 } } { 3 } ; Length of conjugate axis: 2 ; Eccentricity: 2 ; Asymptotes: y = \pm \frac { \sqrt { 3 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . D) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 7 } } { 7 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x .$ 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) $Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 7 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x . B) vertices: \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ; Foci: \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ; Length of transverse axis: \frac { \sqrt { 3 } } { 3 } ; Length of conjugate axis: 2 ; Eccentricity: 2 ; Asymptotes: y = \pm \frac { \sqrt { 3 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . D) vertices: \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 7 } } { 7 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 7 } x . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ; length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 7 } } { 7 } ; Eccentricity: \frac { \sqrt { 70 } } { 7 } ; Asymptotes: y = \pm \frac { \sqrt { 21 } } { 3 } x .$ 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

Use the Given Information to Find the Equation of the Ellipse

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