Explanation Given: The given equation for hyperbola is, 4 x 2 − 9 y 2 = 16 Concept: The general formula for hyperbola equation, A x 2 − B y 2 = C Here, C is constant term. To find the x -intercept, Substitute 0 for y in the general equation of hyperbola and solve for x as follows, A x 2 − B ( 0 ) 2 = C To find y -intercepts, Substitute 0 for x in the general equation of hyperbola 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, 4 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 4 , B is 9 and C is 16 . Calculate the x -intercepts, Substitute 0 for y in equation ( 1 ) . 4 x 2 − 9 ( 0 ) 2 = 16 x 2 = 16 4 x = ± 2 Thus the x -intercepts of the hyperbola are ( 2 , 0 ) and ( − 2 , 0 )

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ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 8.4, Problem 4PS

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The intercepts and the equation of the asymptotes for the given hyperbola

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The intercepts and the equation of the asymptotes for the given hyperbola

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

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

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Chapter 8 Solutions

To find:

The intercepts and the equation of the asymptotes for the given hyperbola