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Graph the Hyperbola 3y2−11x2=13 y ^ { 2 } - 11 x ^ { 2 } = 1

Question 14

Multiple Choice

Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3y2−11x2=13 y ^ { 2 } - 11 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 } - 11 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 11 } } { 11 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . B) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . D) 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 . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . vertices: (±1111,0) \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ;
Foci: (±46233,0) \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ;
Length of transverse axis: 21111\frac { 2 \sqrt { 11 } } { 11 } ;
Length of conjugate axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Eccentricity: 15411\frac { \sqrt { 154 } } { 11 } ;
Asymptotes: y=±3311xy = \pm \frac { \sqrt { 33 } } { 11 } 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 } - 11 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 11 } } { 11 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . B) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . D) 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 . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . vertices: (±1111,0) \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ;
Foci: (±46233,0) \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ;
Length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 21111\frac { 2 \sqrt { 11 } } { 11 } ;
Eccentricity: 15411\frac { \sqrt { 154 } } { 11 } ;
Asymptotes: y=±333xy = \pm \frac { \sqrt { 33 } } { 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 } - 11 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 11 } } { 11 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . B) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . D) 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 . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . vertices: (0,±33) \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ;
Foci: (0,±46233) \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ;
Length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 21111\frac { 2 \sqrt { 11 } } { 11 } ;
Eccentricity: 15411\frac { \sqrt { 154 } } { 11 } ;
Asymptotes: y=±333xy = \pm \frac { \sqrt { 33 } } { 3 } 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 } - 11 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 11 } } { 11 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . B) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . D) 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 . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } 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 .
E) Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 3 y ^ { 2 } - 11 x ^ { 2 } = 1 A) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 11 } } { 11 } ; Length of conjugate axis: \frac { 2 \sqrt { 3 } } { 3 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . B) vertices: \left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right) ; Foci: \left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . C) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 3 } x . D) 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 . E) vertices: \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ; Foci: \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ; Length of transverse axis: \frac { 2 \sqrt { 3 } } { 3 } ; Length of conjugate axis: \frac { 2 \sqrt { 11 } } { 11 } ; Eccentricity: \frac { \sqrt { 154 } } { 11 } ; Asymptotes: y = \pm \frac { \sqrt { 33 } } { 11 } x . vertices: (0,±33) \left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right) ;
Foci: (0,±46233) \left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right) ;
Length of transverse axis: 233\frac { 2 \sqrt { 3 } } { 3 } ;
Length of conjugate axis: 21111\frac { 2 \sqrt { 11 } } { 11 } ;
Eccentricity: 15411\frac { \sqrt { 154 } } { 11 } ;
Asymptotes: y=±3311xy = \pm \frac { \sqrt { 33 } } { 11 } x .

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