To find: The value of a such that the family of the curves are orthogonal trajectories.
Answer to Problem 46E
The curves are orthogonal trajectories when the value of
Explanation of Solution
Given:
The curves are
Derivative rules:
Chain rule:
Calculation:
Obtain the derivative of the curves.
Consider the curve
Differentiate implicitly with respect to x,
Thus, the derivative of the function
That is, the slope of the tangent to the curve
Consider the curve
Differentiate implicitly with respect to x,
Thus the derivative of the function
That is, the slope of the tangent to the curve
Since the curves are orthogonal trajectories, the product of its slope is -1.
Since
Therefore, the curves are orthogonal trajectories when the value of
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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