1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Using the point P(x, y) and the rotation information, find the coordinates of P in the rotated x’y’ coordinate system. 33.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 673 Identify the type of conic, and rotate the coordinate system to eliminate the xy- term. Write and graph the transformed equation. 37.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 673 Identify the type of conic, solve for y, and graph the conic. Approximate the angle of rotation needed to eliminate the xy-term. 41.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 45.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 49.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 673 53. Find the center, vertices, and foci of the hyperbola in the original coordinate system.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 673 53. Find the center, vertices, and foci of the hyperbola in the original coordinate system.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 673 57. True, because there is no xy term to cause a rotation.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page 673 61. A. (1±4, –2) B. (1±3, –2) C. (4±1, 3) D. (4±2, 3) E. (1, –2±3)

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.5 Polar Equations of Conics

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 11 Quick Review

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 12 Quick Review Solutions

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 13 What you’ll learn about Eccentricity Revisited Writing Polar Equations for Conics Analyzing Polar Equations of Conics Orbits Revisited … and why You will learn the approach to conics used by astronomers.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 Focus-Directrix Definition Conic Section A conic section is the set of all points in a plane whose distances from a particular point (the focus) and a particular line (the directrix) in the plane have a constant ratio. (We assume that the focus does not lie on the directrix.)

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Focus-Directrix Eccentricity Relationship

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 A Conic Section in the Polar Plane

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Three Types of Conics for r = ke/(1+ecosθ)

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Polar Equations for Conics

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 19 Example Writing Polar Equations of Conics

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 20 Example Identifying Conics from Their Polar Equations

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 21 Example Matching Graphs of Conics with Their Polar Equations

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 22 Example Finding Polar Equations of Conics

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 23 Example Finding Polar Equations of Conics

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 24 Homework Homework #23 Review Section 8.5 Page 682, Exercises: 1 – 29(EOO) Quiz next time

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 25 Semimajor Axes and Eccentricities of the Planets

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 26 Ellipse with Eccentricity e and Semimajor Axis a