1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 9.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 673 Write an equation in standard form for the conic shown. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 673 Using the point P(x, y) and the translation information given, find coordinates of P in the translated x’y’ coordinate system.. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 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.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 10 Rotation of Cartesian Coordinate Axes

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 11 Rotation of Cartesian Coordinate Axes

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 12 Rotation-of-Axes Formulas

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

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 Coefficients for a Conic in a Rotated System

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Angle of Rotation to Eliminate the Cross- Product Term

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 Discriminant Test

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Example Using Discriminant Test

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Conics and the Equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 19 Homework Homework Assignment #21 Read Section 8.5 Page 673, Exercises: 33 – 61(EOO)

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

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 21 Quick Review

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 22 Quick Review Solutions

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 23 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.

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 24 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.)

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 25 Focus-Directrix Eccentricity Relationship

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 26 The Geometric Structure of a Conic Section

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 27 A Conic Section in the Polar Plane

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 28 Three Types of Conics for r = ke/(1+ecosθ)

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 29 Polar Equations for Conics

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 30 Example Writing Polar Equations of Conics

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 31 Example Writing Polar Equations of Conics

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 32 Example Identifying Conics from Their Polar Equations

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 33 Example Identifying Conics from Their Polar Equations

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 34 Semimajor Axes and Eccentricities of the Planets

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 35 Ellipse with Eccentricity e and Semimajor Axis a