Explanation Definition used: Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the x-axis: An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( − c , 0 ) and ( c , 0 ) , and vertices at ( − a , 0 ) and ( a , 0 ) is x 2 a 2 − y 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along x axis and a conjugate axis at ( 0 , ± b ) . Calculation: The given equation of the hyperbola is x 2 16 − y 2 4 = 1 . Compare the given equation x 2 16 − y 2 4 = 1 with the general equation of hyperbola x 2 a 2 − y 2 b 2 = 1 , the center of the hyperbola is ( 0 , 0 ) and the value of a 2 = 16 and b 2 = 4 . Obtain the value of a and b from a 2 = 16 and b 2 = 4 . a 2 = 16 and b 2 = 4 a = 16 and b = 4 a = 4 and b = 2 Since the value of a is 5, the vertices are ( − 4 , 0 ) and ( 4 , 0 )

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.6, Problem 4E

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The vertices, and foci of the hyperbola x216−y24=1 and sketch the curve.

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Chapter 21 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The vertices, and foci of the hyperbola x 2 16 − y 2 4 = 1 and sketch the curve.

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