Explanation Given: The foci are ( 0 , ± 1 ) , and the length of the transverse axis is 1 . Approach: The general equation of a hyperbola with y -axis as transverse axis is given by ( y − k ) 2 a 2 − ( x − h ) 2 b 2 = 1 ... ( 1 ) b 2 = c 2 − a 2 ... ( 2 ) l = 2 a ... ( 3 ) Here, a is the transverse axis and b is the conjugate axis and c is the focus and ( h , k ) is the center of the hyperbola and l is the length of transverse axis. Calculation: Since, foci are ( 0 , ± 1 ) . Use the midpoint formula to find h and k . ( h + h 2 , k + c + k − c 2 ) = ( 0 + 0 2 , 1 − 1 2 ) ( h , k ) = ( 0 , 0 ) So, h = 0 , k = 0 Since, the length of transverse axis is 1 . Then,

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 12.3, Problem 50E

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The equation for the hyperbola when the foci are (0,±1), and the length of the transverse axis is 1.

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Chapter 12.3, Problem 49E

Chapter 12.3, Problem 51E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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The equation for the hyperbola when the foci are ( 0 , ± 1 ) , and the length of the transverse axis is 1 .

Solution Summary: The author explains the equation of a hyperbola where the foci are (0,pm 1) and the length of the transverse axis is 1

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To find:

The equation for the hyperbola when the foci are (0,±1), and the length of the transverse axis is 1.

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Chapter 12 Solutions

The equation for the hyperbola when the foci are ( 0 , ± 1 ) , and the length of the transverse axis is 1 .

Solution Summary: The author explains the equation of a hyperbola where the foci are (0,pm 1) and the length of the transverse axis is 1

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To find: The equation for the hyperbola when the foci are (0,±1), and the length of the transverse axis is 1.

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Chapter 12 Solutions

To find:

The equation for the hyperbola when the foci are (0,±1), and the length of the transverse axis is 1.