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 ) of length 2 b . “ 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 ) of length 2 b . Calculation: Given that the center is at ( 0 , 0 ) and passes through the points ( 5 , 4 ) and ( 3 , 4 5 5 ) . Substitute ( x , y ) = ( 5 , 4 ) in x 2 a 2 − y 2 b 2 = 1 as, x 2 a 2 − y 2 b 2 = 1 5 2 a 2 − 4 2 b 2 = 1 25 a 2 − 16 b 2 = 1 25 b 2 &#

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

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 21.6, Problem 23E

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The equation of the hyperbola that passes through with (5,4) and (3,455).

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Chapter 21.6, Problem 22E

Chapter 21.6, Problem 24E

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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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The equation of the hyperbola that passes through with ( 5 , 4 ) and ( 3 , 4 5 5 ) .

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The equation of the hyperbola that passes through with (5,4) and (3,455).

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Chapter 21 Solutions