Concept explainers
a.
To determine the equation of the ancillary circle.
a.
Answer to Problem 48E
The equation of the ancillary circle is
Explanation of Solution
Given information:
The radius of the ancillary circle is equal to half the length of the minor axis and center is the same as the ellipse. The ancillary circle is the largest circle that can fit inside an ellipse.
The equation of the ellipse is
Calculation:
The value of
Radius of the circle is half the length of the minor axis:
The radius of the circle is
The equation of the circle can be found by:
Hence, the equation of the ancillary circle is
b.
To show that for a point
b.
Explanation of Solution
Given information:
The equation of the ellipse is
The equation of the ancillary circle is
Proof:
The equation of the circle can be written by using the coordinates
The equation of the ellipse can be written by using the coordinates
Comparing the equations
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