Graph the Hyperbola $x ^ { 2 } - y ^ { 2 } - 2 x + 4 y - 19 = 0$

question 23

Multiple Choice

Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. $x ^ { 2 } - y ^ { 2 } - 2 x + 4 y - 19 = 0$

• A) center: \(( - 1 , - 2 )\) ; vertices: \(( - 5 , - 2 ) , ( 3 , - 2 )\) ; Foci: \(( - 1 \pm 4 \sqrt { 2 } , - 2 )\) ; Length of transverse axis: 8; Length of conjugate axis: 8; Eccentricity: \(\sqrt { 2 }\) ; Asymptotes: \(y = - x - 3 , y = x - 1\) .
• B) Center: \(( - 1 , - 2 )\) ; Vertices: \(( - 1 , - 6 ) , ( - 1,2 )\) ; Foci: \(( - 1 , - 2 \pm 4 \sqrt { 2 } )\) ; length of transverse axis: 8; Length of conjugate axis: 8; Eccentricity: \(\sqrt { 2 }\) ; Asymptotes: \(y = - x - 3 , y = x - 1\) .
• C) center: \(( 1,2 )\) ; vertices: \(( 1 , - 2 ) , ( 1,6 )\) ; Foci: \(( 1,2 \pm 4 \sqrt { 2 } )\) ; Length of transverse axis: 4; Length of conjugate axis: 4; Eccentricity: \(2\) ; Asymptotes: \(y = - x + 3 , y = x + 1\) .
• D) center: \(( 1,2 )\) ; vertices: \(( 1 , - 2 ) , ( 1,6 )\) ; Foci: \(( 1,2 \pm 4 \sqrt { 2 } )\) ; Length of transverse axis: 8; Length of conjugate axis: 8; Eccentricity: \(\sqrt { 2 }\) ; Asymptotes: \(y = - x + 3 , y = x + 1\) .
• E) center: \(( 1,2 )\) ; vertices: \(( - 3,2 ) , ( 5,2 )\) ; Foci: \(( 1 \pm 4 \sqrt { 2 } , 2 )\) ; Length of transverse axis: 8; Length of conjugate axis: 8; Eccentricity: \(\sqrt { 2 }\) ; Asymptotes: \(y = - x + 3 , y = x + 1\) .

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