1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.4 Translations and Rotations of Axes

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Quick Review Solutions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 What you’ll learn about Second-Degree Equations in Two Variables Translating Axes versus Translating Graphs … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Example Plotting Conics

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Example Writing Conic Equations From Graphs

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Translation-of-Axes Formulas

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Translation of Cartesian Coordinate Axes

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Example Finding Coordinates of a Point in a Translated Coordinate System Using the point P (x, y) and the translation information, find the coordinates of P in the translated x’y’ coordinate system. 20.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 10 Example Translation Formula

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 11 Homework Homework Assignment #24 Review Section 8.4 Page 673, Exercises: 1 – 29(EOO)

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 12 What you’ll learn about 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.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 13 Rotation of Cartesian Coordinate Axes

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 Rotation-of-Axes Formulas

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Example Rotation of Axes

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 Coefficients for a Conic in a Rotated System

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Angle of Rotation to Eliminate the Cross- Product Term

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Discriminant Test

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 19 Example Using Discriminant Test

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 20 Conics and the Equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0