Concept explainers
Find the center, vertices, foci and eccentricity of the ellipse and sketch the ellipse
Answer to Problem 42E
Center:
Vertices:
Foci:
Eccentricity:
Given:
The given equation is
Explanation:
Simplifying the given equation,
The given equation represents an ellipse with major axis vertical.
The standard equation of an ellipse with major axis vertical is given by
Comparing this with equation (1),
Thus, the center of the ellipse is
Now, since the vertices are at
Next,
Thus,
The foci lie on the points
The foci are at
The eccentricity of the ellipse is given by
Thus,
The graph of the given ellipse is depicted below:
Explanation of Solution
Given:
The given equation is
Simplifying the given equation,
The given equation represents an ellipse with major axis vertical.
The standard equation of an ellipse with major axis vertical is given by
Comparing this with equation (1),
Thus, the center of the ellipse is
Now, since the vertices are at
Next,
Thus,
The foci lie on the points
The foci are at
The eccentricity of the ellipse is given by
Thus,
The graph of the given ellipse is depicted below:
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
- 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