1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 653 Find the vertices and foci of the ellipse. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 653 Find the vertices and foci of the ellipse. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 653 Match the graph to the equation given that all of the ticks represent one unit. 9. a.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 653 Sketch the graph of the ellipse by hand. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 653 Graph the ellipse using a function grapher. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 33.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 10 Homework, Page 653 Find center, vertices, and foci of the ellipse. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 11 Homework, Page 653 Graph the ellipse using a parametric grapher. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 12 Homework, Page 653 Prove the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 13 Homework, Page 653 Write an equation for the ellipse. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 Homework, Page 653 53.The Moon’s apogee is 252,710 mi, and perigee is 221,463 mi. Assuming the Moon’s orbit is elliptical, with the Earth at one focus, calculate and interpret a, b, c, and e.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Homework, Page 653 57.The sun grazers pass within a Sun’s diameter of the solar surface. What can you conclude about a – c for orbits of sun grazers? (From problem #54, we know that the diameter of the Sun is about 1.392 Gm.)

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 Homework, Page 653 Solve the system of equations algebraically and support your answer graphically. 61.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Homework, Page 653 65.The distance from a focus of an ellipse to the closer vertex is a(1 + e) where a is a semimajor axis and e is the eccentricity. Justify your answer

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Homework, Page 653 69. A. (4, 2) B. (4, 3) C. (4, 4) D. (4, 5) E. (4, 6)

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.3 Hyperbolas

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 20 What you’ll learn about Geometry of a Hyperbola Translations of Hyperbolas Eccentricity and Orbits Reflective Property of a Hyperbola Long-Range Navigation … and why The hyperbola is the least known conic section, yet it is used in astronomy, optics, and navigation.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 21 Hyperbola A hyperbola is the set of all points in a plane whose distances from two fixed points in the plane have a constant difference. The fixed points are the foci of the hyperbola. The line through the foci is the focal axis. The point on the focal axis midway between the foci is the center. The line through the center and perpendicular to the focal axis is the conjugate axis. The points where the hyperbola intersects its focal axis are the vertices of the hyperbola. The line collinear with the focal axis and connecting the vertices is the transverse axis.

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

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

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 24 Hyperbola with Center (0,0)

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 25 Hyperbola Centered at (0,0)

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 26 Example Finding the Vertices and Foci of a Hyperbola

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 27 Example Sketching a Hyperbola by Hand

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 28 Example Finding an Equation of a Hyperbola

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 29 Hyperbola with Center (h,k)

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 30 Hyperbola with Center (h,k)

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 31 Example Locating Key Points of a Hyperbola

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 32 Example Locating a Point Using Hyperbolas Radio signals are sent simultaneously from three transmitters located at O, Q, and R. R is 80 miles due north of O and Q is 100 miles due east of O. A ship receives the transmission from O 323.27 μsec after the signal from R and 258.61 μsec after the signal from Q. What is the ship’s bearing and distance from O?

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 33 Example Locating a Point Using Hyperbolas

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 34 Eccentricity of a Hyperbola

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 35 Homework Homework Assignment #18 Review Section 8.3 Page 663, Exercises: 1 – 65(EOO), skip 53

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

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 37 Quick Review

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 38 Quick Review Solutions

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 39 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.

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 40 Example Plotting Conics

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 41 Example Writing Conic Equations From Graphs

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 42 Translation-of-Axes Formulas

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 43 Translation of Cartesian Coordinate Axes

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 44 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.

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 45 Example Translation Formula