To identify: the graph of the equation.
Answer to Problem 24E
The graph of the equation is a hyperbola
Explanation of Solution
Given:
Calculation:
Given the following equation:
Comparing with the standard equation for a Quadratic Curve,
We get:
For the cross-product term to vanish, the coordinate axes must be rotated by an angle alpha,such that
Therefore,
After rotation of coordinate axes, the original coordinates,
Substituting the above values of
Which is a hyperbola
Conclusion:
The graph of the equation is a hyperbola
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Precalculus (10th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus and Its Applications (11th Edition)
- 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