Explanation Given: The given equation for hyperbola is, 25 y 2 − 3 x 2 = 75 Concept: 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 the 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, 25 y 2 − 3 x 2 = 75 ... ( 1 ) Substitute 0 for y in equation ( 1 ) , 25 ( 0 ) 2 − 3 x 2 = 75 − 3 x 2 = 75 x 2 = − 25 Since, x 2 = − 25 has no real number solution. Hence there is no real x - intercepts for the given hyperbola. Substitute 0 for x in equation ( 1 ) , 25 y 2 − 3 ( 0 ) 2 = 75 y 2 = 75 25 y 2 = 3 y = ± 3 Therefore the y -intercepts points ( 0 , 3 ) and ( 0 , − 3 ) are on the graph. Consider equation ( 1 ) and solve for y yields and set up a table as follows, 25 y 2 − 3 x 2 = 75 25 y 2 = 3 x 2 + 75 y 2 = 3 x 2 + 75 25 y = ± 1 5 3 x 2 + 75 ... ( 2 ) Substitute 1 for x in equation ( 2 ) , y = ± 1 5 3 ( 1 ) 2 + 75 = ± 1 5 3 + 75 = ± 78 5 Plot the point on graph ( 1 , ± 78 5 )

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 8.4, Problem 17PS

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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.

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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.