Graph the Hyperbola $y ^ { 2 } - 4 x ^ { 2 } = 4$

question 15

Multiple Choice

Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. $y ^ { 2 } - 4 x ^ { 2 } = 4$

• A) vertices: \(( 0 , \pm 2 )\) ; Foci: \(( 0 , \pm \sqrt { 5 } )\) ; Length of transverse axis: 4; Length of conjugate axis: 2; Eccentricity: \(\frac { \sqrt { 5 } } { 2 }\) Asymptotes: \(y = \pm 2 x\) .
• B) vertices: \(( 0 , \pm 1 )\) ; Foci: \(( 0 , \pm \sqrt { 5 } )\) ; Length of transverse axis: 2; Length of conjugate axis: 4; Eccentricity: \(\sqrt { 5 }\) ; Asymptotes: \(y = \pm \frac { 1 } { 2 } x\) .
• C) vertices:\(( \pm 2,0 )\) ; Foci: \(( \pm \sqrt { 5 } , 0 )\) ; Length of transverse axis: 4; Length of conjugate axis: 2; Eccentricity: \(\frac { \sqrt { 5 } } { 2 }\) Asymptotes: \(y = \pm \frac { 1 } { 2 } x\) .
• D) vertices:\(( \pm 1,0 )\) ; Foci: \(( \pm \sqrt { 37 } , 0 )\) ; Length of transverse axis: 2; Length of conjugate axis: 12; Eccentricity: \(\sqrt { 37 }\) ; Asymptotes: \(y = \pm 37 x\) .
• E) vertices: \(( \pm 1,0 )\) ; Foci: \(( \pm \sqrt { 5 } , 0 )\) ; Length of transverse axis: 2; Length of conjugate axis: 4; Eccentricity: \[\sqrt { 5 }\] Asymptotes: \(y = \pm 2 x\) .

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