1. Copyright © 2011 Pearson, Inc. 8.4 Translation and Rotation of Axes

2. Copyright © 2011 Pearson, Inc. Slide 8.4 - 2 What you’ll learn about Second-Degree Equations in Two Variables Translating Axes versus Translating Graphs Rotation of Axes Discriminant Test … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.

3. Copyright © 2011 Pearson, Inc. Slide 8.4 - 3 Example Graphing a Second-Degree Equation

4. Copyright © 2011 Pearson, Inc. Slide 8.4 - 4 Example Graphing a Second-Degree Equation

5. Copyright © 2011 Pearson, Inc. Slide 8.4 - 5 Example Graphing a Second-Degree Equation

6. Copyright © 2011 Pearson, Inc. Slide 8.4 - 6 Example Graphing a Second-Degree Equation

7. Copyright © 2011 Pearson, Inc. Slide 8.4 - 7 Translation-of-Axes Formulas

8. Copyright © 2011 Pearson, Inc. Slide 8.4 - 8 Example Translation Formula

9. Copyright © 2011 Pearson, Inc. Slide 8.4 - 9 Example Translation Formula

10. Copyright © 2011 Pearson, Inc. Slide 8.4 - 10 Example Translation Formula

11. Copyright © 2011 Pearson, Inc. Slide 8.4 - 11 Rotation-of-Axes Formulas

12. Copyright © 2011 Pearson, Inc. Slide 8.4 - 12 Rotation of Cartesian Coordinate Axes

13. Copyright © 2011 Pearson, Inc. Slide 8.4 - 13 Example Rotation of Axes

14. Copyright © 2011 Pearson, Inc. Slide 8.4 - 14 Example Rotation of Axes

15. Copyright © 2011 Pearson, Inc. Slide 8.4 - 15 Example Rotation of Axes

16. Copyright © 2011 Pearson, Inc. Slide 8.4 - 16 Coefficients for a Conic in a Rotated System

17. Copyright © 2011 Pearson, Inc. Slide 8.4 - 17 Angle of Rotation to Eliminate the Cross-Product Term

18. Copyright © 2011 Pearson, Inc. Slide 8.4 - 18 Discriminant Test

19. Copyright © 2011 Pearson, Inc. Slide 8.4 - 19 Conics and the Equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0

20. Copyright © 2011 Pearson, Inc. Slide 8.4 - 20 Quick Review

21. Copyright © 2011 Pearson, Inc. Slide 8.4 - 21 Quick Review Solutions