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

question 3

Multiple Choice

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

• 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: \(y = \pm \frac { \sqrt { 21 } } { 3 } x\) .

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