Explanation Given: The given equation for hyperbola is, 9 x 2 − 4 y 2 = 9 Approach: The formula of hyperbola that is symmetric with respect to the origin is as follows, A x 2 − B y 2 = C Here, C is constant term and A , B and C are nonzero real numbers. To find the x -intercept, Substitute 0 for y in 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 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 given hyperbola equation, 9 x 2 − 4 y 2 = 9 ... ( 1 ) Substitute 0 for y in equation ( 1 ) , 9 x 2 − ( 0 ) 2 = 9 9 x 2 = 9 x = ± 1 Therefore the x -intercepts points ( 1 , 0 ) and ( − 1 , 0 ) are on the graph. Substitute 0 for x in equation ( 1 ) , ( 0 ) 2 − 4 y 2 = 9 y 2 = − 9 4 Since, y 2 = − 9 4 has no real number solution. Hence there is no real y - intercepts for the given hyperbola. Consider equation ( 1 ) and solve for y yields and set up a table as follows, 9 x 2 − 4 y 2 = 9 − 4 y 2 = 9 − 9 x 2 y 2 = 9 x 2 − 9 4 y = ± 3 2 x 2 − 1 ... ( 2 ) Substitute 2 for x in equation ( 2 ) , y = ± 3 2 ( 2 ) 2 − 1 = ± 3 2 4 − 1 = ± 3 3 2 Plot the point on graph ( 2 , ± 3 3 2 )

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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 12PS

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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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To plot: The graph for given equation of hyperbola.

Solution Summary: The author explains the formula of hyperbola that is symmetric with respect to the origin is as follows: A, B and C are nonzero real numbers.

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To plot: The graph for given equation of hyperbola.

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Chapter 8 Solutions

To plot:

The graph for given equation of hyperbola.