Concept explainers
(a)
To find out how the plane curves differ from each other.
(a)
Explanation of Solution
Given Information:
The given curve is-
The given curve is-
Now, the equations are polynomial in and hence are defined for all values of
Therefore, there are no restrictions on the values of and
The graph of the parametric curve is shown below.
Therefore, the domain is
Therefore, the orientation is downwards or from left to right.
Now, eliminate the parameter.
Substitute the value of from the first equation into second equation.
Therefore, the rectangular equation is
To find out how the plane curves differ from each other.
Explanation of Solution
Given Information:
The given curve is-
Calculation:
The given curve is-
Therefore, the domain is-
The graph of the parametric curve is shown below-
The orientation of the curve is upwards.
Now, eliminating the parameter and substitute the value of from the equation into second equation. Therefore, the rectangular equation is
To find out how the plane curves differ from each other.
Explanation of Solution
Given Information:
The given curve is-
The given curve is-
Since,
Therefore, the domain is
The graph of the parametric curve is shown below.
The orientation of the curve is downwards or from left to right.
Therefore, the rectangular equation is-
To find out how the plane curves differ from each other.
Explanation of Solution
Given Information:
The given curve is-
Calculation:
The given curve is-
Since,
Therefore, the domain is
The sketch is shown below-
Therefore, the orientation is upwards.
Now, eliminating the parameter.
Substituting the value of from the first equation into second equation.
Therefore, the rectangular equation is-
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