To derive: formulas for the focal width of an ellipse and the focal width of a hyperbola.
The focal width is
Formula used:
Polar equation:
Polar equation:
Calculation:
The focal width lies in the line
For
For
The endpoints are
The focal width is the sum of the two
The polar equation:
The focus is at the pole with the focal axis. The focal width lies on the
Substitute
Substitute
The endpoints are
The focal width is the sum of the
Hence, the focal width is
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