Concept explainers
a.
To Graph: The given equation for different value of k.
a.
Answer to Problem 53RE
The obtained graph is,
Explanation of Solution
Given information:
The function is
Calculation:
The obtained graph is.
Interpretation:
The center for all the ellipse is origin
b.
To prove: All the ellipse in (a) have same foci.
b.
Answer to Problem 53RE
All the ellipse have same foci.
Explanation of Solution
Given information:
The given family of ellipse are
Calculation:
For
Here
We know that the distance from each focus to the center, given semi major axis a or semi minor axis b, is
Foci are
For
Here
Foci are
For
Here
Foci are
For
Here
Foci are
Hence all the ellipse have same foci.
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th 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