Explanation Given: The given equation is, 9 x 2 − y 2 = 81 Procedure used: The general equation of hyperbola is, A x 2 − B y 2 = C Here, C is a constant term. 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 . A x 2 − B y 2 = 0 Calculate y- intercept by substituting 0 for x in the standard equation of hyperbola. Calculate x- intercept by substituting 0 for y in the standard equation of hyperbola. Calculation: Consider the equation. 9 x 2 − y 2 = 81 ... ( 1 ) Calculate the y -intercepts as shown. Substitute 0 for x in equation ( 1 ) . 9 ( 0 ) 2 − y 2 = 81 − y 2 = 81 y 2 = − 81 This gives an imaginary number. Thus, the hyperbola does not intersect the y -axis. Calculate the x -intercepts as shown. Substitute 0 for y in equation ( 1 ) . 9 x 2 − ( 0 ) 2 = 81 9 x 2 = 81 x 2 = 9 x = ± 3 Thus, the end points of x -intercepts are ( − 3 , 0 ) and ( 3 , 0 ) , and the points are on the graph. Find the asymptotes of equation ( 1 ) . Substitute 0 for the constant term in equation ( 1 ) and solve for y . 9 x 2 − y 2 = 0 9 x 2 = y 2 ± 9 x 2 = y ± 3 x = y Thus, the asymptotes are y = 3 x and y = − 3 x

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 8.CR, Problem 32CR

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The equation 9x2−y2=81.

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Intermediate Algebra

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