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Graph the Hyperbola 3y2−7x2=13 y ^ { 2 } - 7 x ^ { 2 } = 1

Question 3

Multiple Choice

Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3y2−7x2=13 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: (±77,0) \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ;
Foci: (±21021,0) \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ;
Length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 277\frac { 2 \sqrt { 7 } } { 7 } ;
Eccentricity: 707\frac { \sqrt { 70 } } { 7 } ;
Asymptotes: y=±213xy = \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: (±36,0) \left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right) ;
Foci: (±233,0) \left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right) ;
Length of transverse axis: 33\frac { \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 22 ;
Eccentricity: 22 ;
Asymptotes: y=±33xy = \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: (0,±33) \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ;
Foci: (0,±21021) \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ;
Length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 277\frac { 2 \sqrt { 7 } } { 7 } ;
Eccentricity: 707\frac { \sqrt { 70 } } { 7 } ;
Asymptotes: y=±217xy = \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: (±77,0) \left( \pm \frac { \sqrt { 7 } } { 7 } , 0 \right) ;
Foci: (±21021,0) \left( \pm \frac { \sqrt { 210 } } { 21 } , 0 \right) ;
Length of transverse axis: 277\frac { 2 \sqrt { 7 } } { 7 } ;
Length of conjugate axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Eccentricity: 707\frac { \sqrt { 70 } } { 7 } ;
Asymptotes: y=±217xy = \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: (0,±33) \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ;
Foci: (0,±21021) \left( 0 , \pm \frac { \sqrt { 210 } } { 21 } \right) ;
length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 277\frac { 2 \sqrt { 7 } } { 7 } ;
Eccentricity: 707\frac { \sqrt { 70 } } { 7 } ;
Asymptotes: y=±213xy = \pm \frac { \sqrt { 21 } } { 3 } x .

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