Concept explainers
The standard equation and then sketch the graph for the given cases.
Explanation of Solution
Given:
The expression is given as;
Rotation of axes to eliminate xy term:
The general second degree equation
By rotating the coordinate axes through an angle
Where,
The coefficients of the new equation are obtained by making the following substitutions
And
Consider the equation of the conic
Here A=C=2,B=1,D=E=0 and F=-8
The transformed equation is
Further simplify as shown below
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