How the given graph is similar to and different to a full-fledged hyperbola.
It has been explained how the given graph is similar to and different to a full-fledged hyperbola.
Given:
The graph of the equation,
Concept used:
A hyperbola is formed when a plane intersects a double-sided cone in both nappes.
Calculation:
The given equation is
Simplifying,
On further simplification,
Continuing simplification,
Finally,
This is the equation of a pair of straight lines; having slope
So, the graph of the given equation is a pair of straight lines; having slope
Now, as discussed, a hyperbola is formed when a plane intersects a double-sided cone in both nappes.
This is true for both a full-fledged hyperbola and the above equation.
The difference lies in the fact that the graph of the above equation is formed when the plane passes through the vertex of the cone.
Conclusion:
It has been explained how the given graph is similar to and different to a full-fledged hyperbola.
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- 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
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