(a)
To find: The standard equation of hyperbola
(a)
Answer to Problem 34E
The standard form of the hyperbola is
Explanation of Solution
Given information:
The given equation of the hyperbola is
Calculation:
Write the equation of the hyperbola.
Therefore, the standard form of the hyperbola is
(b)
To find: The center, vertices, foci, asymptotes of the hyperbola
(b)
Answer to Problem 34E
The center of the hyperbola is
Explanation of Solution
Given information:
Given equation of hyperbola is
Calculation:
Compare the given equation with the standard equation of hyperbola
The center of the hyperbola is given as
The vertices of the hyperbola is given by
So the vertices are
The foci of the hyperbola is given by
Hence the foci are
The asymptotes of the hyperbola is given by
Substitute
Therefore The center of the hyperbola is
(c)
To draw: The graph of the hyperbola
(c)
Answer to Problem 34E
The graph of the hyperbola is shown in figure (1).
Explanation of Solution
Given information: The equation of the hyperbola is
Calculation:
To draw the graph of hyperbola, solve the equations of hyperbola in terms of
Take square root on both the sides and simplify.
Use the above equation and the asymptotes to draw the graph of the hyperbola.
Figure (1)
Therefore, the graph of the hyperbola is shown in figure (1).
Verify the result using graphical utility:
Draw the graph for the hyperbola using the graphical utility.
From the above, it is clear that both the graphs are similar.
Hence, proved.
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning