To determine The vertices and foci of the hyperbola y 2 4 − x 2 21 = 1 and sketch the curve. Explanation Definition used: “ Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the y-axis An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( 0 , − c ) and ( 0 , c ) , and vertices at ( 0 , − a ) and ( 0 , a ) is y 2 a 2 − x 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along y axis and a conjugate axis at ( ± b , 0 ) . Calculation: The given equation of the hyperbola is y 2 4 − x 2 21 = 1 . Compare the given equation y 2 4 − x 2 21 = 1 with the general equation of hyperbola y 2 a 2 − x 2 b 2 = 1 , the center of the hyperbola is ( 0 , 0 ) and the value of a 2 = 4 and b 2 = 21 . Obtain the value of a and b from a 2 = 4 and b 2 = 21 . a 2 = 4 and b 2 = 21 a = 4 and b = 21 a = 2 and b = 21 Since the value of a is 2, the vertices are ( 0 , − 2 ) and ( 0 , 2 )

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 21.6, Problem 6E

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The vertices and foci of the hyperbola y24−x221=1 and sketch the curve.

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Chapter 21.6, Problem 5E

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Chapter 21 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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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