Concept explainers
To graph the curve represented by the parametric equations.
Explanation of Solution
Given information:
Given parametric equation is
.
Calculation:
The parametric equations are defined for all values of the parameter
Let us find the rectangular equation by eliminating the parameter
From the first of the parametric equations,
Similarly from the second equation
Use the trigonometric identity
This is the equation of an ellipse. It is known that equation of an ellipse having centre at
The vertices and foci of this ellipse are
Vertices:
Foci:
Comparing equation (2) with the standard equation of an ellipse given by equation (3), it is seen that the ellipse represented by equation (2) has centreat
Using graphing utility, the graph of the ellipse is drawn in the viewing window
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