Concept explainers
Rotate the axes to eliminate the xy-term in the equation and write the equation in standard form. Sketch the graph of the resulting equation, shaming both sets of axes.
Answer to Problem 23E
The required equation in standard form is
Explanation of Solution
Given:
The equation of the conic
Rotation of axes to eliminate xy-term:
The general second-degree equation
By rotating the coordinate axes through an angle
The coefficients of the new equation are obtained by making the following substitutions
And
Consider the equation of the conic
Here
Further solve as shown below:
Also the value is as below:
The transformed equation is
And the equation becomes:
Thus the required equation in standard form is
The graph of
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