Explanation Property used: Hyperbola with center at the origin: Center Transverse Axis Branches Open Foci Vertices Equation ( 0 , 0 ) x -axis Left and right ( − c , 0 ) and ( c , 0 ) ( − a , 0 ) and ( a , 0 ) x 2 a 2 − y 2 b 2 = 1 , where c 2 = a 2 + b 2 ( 0 , 0 ) y -axis Up and down ( 0 , − c ) and ( 0 , c ) ( 0 , − a ) and ( 0 , a ) y 2 a 2 − x 2 b 2 = 1 , where c 2 = a 2 + b 2 Calculation: Since one vertex is at ( 2 , 0 ) the other vertex must be at ( − 2 , 0 ) . Observe that, the vertices ( − 2 , 0 ) and ( 2 , 0 ) , and the focus ( 3 , 0 ) are points on the x -axis. Therefore, x -axis is the transverse axis and the hyperbola opens left and right. Since a vertex is ( 2 , 0 ) , a = 2 and since the focus is at ( 3 , 0 ) , c = 3 . b 2 = c 2 − a 2 b 2 = 3 2 − 2 2 b 2 = 9 − 4 b 2 = 5 The required equation is of the form x 2 a 2 − y 2 b 2 = 1 . Since, a 2 = 4 and b 2 = 5 , the required equation is x 2 4 − y 2 5 = 1

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ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter 12.5, Problem 23E

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The equation of a hyperbola whose center is at (0,0) vertex at (2,0); focus at (3,0), and graph the same.

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Chapter 12.5, Problem 22E

Chapter 12.5, Problem 24E

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The equation of a hyperbola whose center is at ( 0 , 0 ) vertex at ( 2 , 0 ) ; focus at ( 3 , 0 ) , and graph the same.

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The equation of a hyperbola whose center is at (0,0) vertex at (2,0); focus at (3,0), and graph the same.

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