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 )

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

See similar textbooks

Videos

Question

Chapter 8.4, Problem 1PS

To determine

To find:

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 10CQ

Chapter 8.4, Problem 2PS

Students have asked these similar questions

3. Write a system of linear equations in slope intercept form that has exactly one solution at the point (3, 4), such that one line has positive slope (but not 1) and the other line has negative slope (but not "1). Also write your system of equations with both equations written in standard form with out any fractions 8- 7 8 5 4 3 -2- + -8-7-6-5-4-3-2-1 1 2 3 -1 2 - ° 4 -5 - -8

2. Write a system of linear equations in slope-intercept form has exactly one solution at the point (3, 4), such that both lines have negative slope (but neither one has slope of 1). Also write your system of equations with both equations written in standard form without any fractions. B 0 5 4 3 -2 1 -8-7-6-5-4-3-2 -1 12 3 -1 2 -3 -5 6 -7 -8

4. Write a system of linear equations in slope-intercept form that has no solution, such that (3, 4), and (3,8) are solutions to the first equation, and (0, 4) is a solution to the second equation. Also write your system of equations with both equations written in standard form with out any fractions B 0 5 4 3 -2 + -8-7-6-5-4-3-2 -1 |- 1 2 3 -1 2 -3 4 -5 6 -7

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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

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

Videos

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

Want to see the full answer?

Chapter 8 Solutions

To find:

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