Explanation Given: The given equation for hyperbola is, x 2 − 9 y 2 = 16 Method: The general equation of hyperbola, A x 2 + B y 2 = C Here, C is constant term. To find the x -intercept, Substitute 0 for y in the hyperbola equation and solve for x as follows, A x 2 + B ( 0 ) 2 = C To find y -intercepts, Substitute 0 for x in the hyperbola equation and solve for y as follows, A ( 0 ) 2 + B y 2 = C To find the equation for the asymptotes replace the constant term of A x 2 + B y 2 = C with 0 and solve for y as follows, A x 2 + B y 2 = 0 Calculation: Consider the hyperbola equation, x 2 − 9 y 2 = 16 → ( 1 ) Compare above equation with general equation A x 2 + B y 2 = C . The value of A is 1 , B is − 9 and C is 16 . Substitute 0 for y in equation ( 1 ) , x 2 − 9 ( 0 ) 2 = 16 x 2 = 16 x = ± 4 Thus the x - intercepts of the hyperbola are ( − 4 , 0 ) and ( 4 , 0 )

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Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 8.4, Problem 1PS

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The intercepts and the equations of the asymptotes for the given hyperbola.

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Chapter 8.4, Problem 10CQ

Chapter 8.4, Problem 2PS

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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 intercepts and the equations of the asymptotes for the given hyperbola.

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To find: The intercepts and the equations of the asymptotes for the given hyperbola.

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Chapter 8 Solutions

To find:

The intercepts and the equations of the asymptotes for the given hyperbola.