Explanation Given: The given equation for hyperbola is, y 2 − 16 x 2 = 4 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 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 the 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, y 2 − 16 x 2 = 4 ... ( 1 ) Substitute 0 for y in equation ( 1 ) , ( 0 ) x 2 − 16 x 2 = 4 − 16 x 2 = 4 x 2 = − 4 16 x 2 = − 1 4 Since, x 2 = − 1 4 has no real number solution. Hence there is no real x - intercepts for the given hyperbola. Substitute 0 for x in equation ( 1 ) , y 2 − 16 ( 0 ) 2 = 4 y 2 = 4 y = ± 2 Therefore the y -intercepts points ( 0 , 2 ) and ( 0 , − 2 ) are on the graph. Consider equation ( 1 ) and solve for y yields and set up a table as follows, y 2 − 16 x 2 = 4 y 2 = 16 x 2 + 4 y = 16 x 2 + 4 ... ( 2 ) Substitute 1 for x in equation ( 2 ) , y = ± 16 ( 1 ) 2 + 4 = ± 16 + 4 = ± 20 = ± 2 5 Plot the point on graph ( 1 , ± 2 5 )

10th Edition

ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

See similar textbooks

Videos

Question

Chapter 8.4, Problem 13PS

To determine

To plot:

The graph for given equation of hyperbola.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 12PS

Chapter 8.4, Problem 14PS

Students have asked these similar questions

Use grouping to fully factor: x³ + 3x² - 16x - 48 = 0 3 2

Name: Tay Jones Level Two Date: Algebra 3 Unit 3: Functions and Equations Practice Assessment Class: #7-OneNote 1. The function f(x) = x² is transformed in the following functions. List the vertex for each function, circle whether the function opens up or down, and why. All three parts must be correct to receive Level 2 points. You can receive points for a, b, and c. a) g(x) = -2(x+5)² Vertex: Opens Up Opens Down Why? ais negative -2 Vertex: b) g(x) = (x + 2)² - 3 c) g(x) = -4(x + 2)² + 2 Opens Up Opens Down Vertex: Opens Up Opens Down Why? 4 Ca is negative) Why? his positive 2. The graph of the function f(x) is shown below. Find the domain, range, and end behavior. Then list the values of x for which the function values are increasing and decreasing. f(x) Domain: End Behavior: As x → ∞o, f(x) -> -6 As x, f(x) -> Range: Where is it Increasing? (002] Where is it Decreasing? (1,00)

Show what to do on the graph visually please!

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.

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.

Videos

To plot: The graph for given equation of hyperbola.

Want to see the full answer?

Chapter 8 Solutions

To plot:

The graph for given equation of hyperbola.