1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 682 Graph the conic and find the values of e, a, b, and c. 31.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 682 Graph the conic and find the values of e, a, b, and c. 33.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 682 Graph the conic and find the values of e, a, b, and c. 35.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 682 Determine a Cartesian equation for the given polar equation. 37.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Example, Writing Cartesian Equations From Polar Equations Use the fact that k = 2p is twice the focal length and half the focal width to determine the Cartesian equation of the parabola whose polar equation is given. 39.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 682 41. The orbit of Halley’s Comet has a semimajor axis of 18.09 AU ans an orbital eccentricity of 0.97. Compute its perihelion and aphelion distances.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 682 45. True or False. The equation yields no true circles. Justify your answer.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 682 47. Which ratio of distances is constant for a point on a nondegenerate conic? A.distance to center : distance to vertex B.distance to focus : distance to vertex C.distance to vertex : distance to directrix D.distance to focus : distance to directrix E.distance to center : distance to vertex

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page 682 49. For a conic expressed by r = ke / (1+ e sin θ) which point is located at the pole? A.the center B.a focus C.a vertex D.an endpoint of the minor axis E.an endpoint of the conjugate axis

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.6 Three-Dimensional Cartesian Coordinate System

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 Three-Dimensional Cartesian Coordinates Distances and Midpoint Formula Equation of a Sphere Planes and Other Surfaces Vectors in Space Lines in Space … and why This is the analytic geometry of our physical world.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 The Point P(x,y,z) in Cartesian Space

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Features of the Three-Dimensional Cartesian Coordinate System The axes are labeled x, y, and z, and these three coordinate axes form a right-handed coordinate frame. The Cartesian coordinates of a point P in space are an ordered triple, (x, y, z). Pairs of axes determine the coordinate planes. The coordinate planes are the xy-plane, the xz-plane, and the yz-plane and they have equations z = 0, y = 0, and x = 0, respectively. The coordinate planes meet at the origin (0, 0, 0). The coordinate planes divide space into eight regions called octants. The first octant contains all points in space with three positive coordinates.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 The Coordinate Planes Divide Space into Eight Octants

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Distance Formula (Cartesian Space)

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Midpoint Formula (Cartesian Space)

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 19 Example Calculating a Distance and Finding a Midpoint

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 20 Standard Equation of a Sphere

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

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 22 Drawing Lesson (cont’d)

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 23 Example Finding the Standard Equation of a Sphere

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 24 Equation for a Plane in Cartesian Space

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 25 Example Sketching a Graph in Three Dimensions Sketch a graph of the equation. Label all intercepts. 18.

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 26 The Vector v =

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 27 Vector Relationships in Space

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 28 Example Evaluating Three Dimensional Vector Expressions

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 29 Example Three-Dimensional Velocity 34.A rocket, soon after launch, is headed east and is climbing at an angle of 20° relative to flat ground with an airspeed of 12,000 mph. If the wind is out of the southwest at 8 mph, calculate a vector v that represents the rocket’s velocity relative to the point of takeoff.

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 30 Equations for a Line in Space

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 31 Example Finding Equations for a Line

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 32 Example Finding Equations for a Line

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 33 Homework Homework Assignment #24 Review Section 8.6 Page 693, Exercises: 1 – 65(EOO) Quiz next time