Explanation Given: The given equation is, 4 x 2 − 24 x − y 2 + 4 y + 28 = 0 Definition: Let complete the square on x and on y and write in the form of general equation of hyperbola as follow, A ( x − h ) 2 − B ( y − k ) 2 = C Here, C is constant term. To find the equation for the asymptotes replace the constant term of A ( x − h ) 2 − B ( y − k ) 2 = C with 0 and solve for y as follows, A ( x − h ) 2 − B ( y − k ) 2 = 0 Calculation: Consider the given equation, 4 x 2 − 24 x − y 2 + 4 y + 28 = 0 ... ( 1 ) Let complete the square on x and on y . 4 x 2 − 24 x − y 2 + 4 y + 28 = 0 4 ( x 2 + 6 x ) − ( y 2 + 4 y ) = − 28 4 ( x 2 + 6 x + 9 ) − ( y 2 − 4 y + 4 ) = − 28 + 36 − 4 Further solve the equation, 4 ( x + 3 ) 2 − ( y − 2 ) 2 = 4 ( 2 ( x + 3 ) ) 2 − ( y − 2 ) 2 = 4 ( 2 x + 6 ) 2 − ( y − 2 ) 2 = 4

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 8.4, Problem 22PS

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The equation of the asymptotes for the given curves.

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Chapter 8.4, Problem 21PS

Chapter 8.4, Problem 23PS

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Chapter 8 Solutions

Intermediate Algebra

Ch. 8.1 - For Problems 110, answer true or false. The graph...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 4CQ Ch. 8.1 - Prob. 5CQ Ch. 8.1 - Prob. 6CQ Ch. 8.1 - Prob. 7CQ Ch. 8.1 - Prob. 8CQ Ch. 8.1 - Prob. 9CQ Ch. 8.1 - Prob. 10CQ

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The equation of the asymptotes for the given curves.

Solution Summary: The author explains how to find the equation of the asymptotes for the given curves.

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To find: The equation of the asymptotes for the given curves.

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Chapter 8 Solutions

To find:

The equation of the asymptotes for the given curves.