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 20E
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 theequationof the conic
Here
Then the value is as shown below
Thetransformedequationis
Further simplifyas shown below:
The equation is solved as:
Thus the required equation in standard form is:
the graphof
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