1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 641 Find the vertex, focus, directrix, and focal width of the parabola. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 641 Find the vertex, focus, directrix, and focal width of the parabola. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 641 Match the graph with its equation. 9. (a)

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 641 Find an equation in standard form for the parabola that satisfies the given conditions. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 641 Find an equation in standard form for the parabola that satisfies the given conditions. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 641 Find an equation in standard form for the parabola that satisfies the given conditions. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 641 Find an equation in standard form for the parabola that satisfies the given conditions. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 641 Find an equation in standard form for the parabola that satisfies the given conditions. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page 641 Sketch the graph of the parabola by hand 33.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 10 Homework, Page 641 Graph the parabola using a function grapher. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 11 Homework, Page 641 Graph the parabola using a function grapher. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 12 Homework, Page 641 Graph the parabola using a function grapher. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 13 Homework, Page 641 Prove that the graph of the equation is a parabola, and find its vertex, focus, and directrix. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 14 Homework, Page 641 Write an equation for the parabola. 53.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 15 Homework, Page 641 57.Explain why the derivation of x 2 = 4py is valid regardless of whether p > 0 or p < 0. The derivation on page 635 only requires that p be a real number, its sign is of no significance in the derivation, although in the equation in standard form it tells us the direction in which the parabola opens.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 16 Homework, Page 641 61.The Sports Channel uses a parabolic microphone to capture the sounds from golf tournaments. If one of its microphones has a parabolic surface generated by the parabola x 2 = 10y, locate the focus (the electronic receiver) of the parabola.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 17 Homework, Page 641 65.Every point on a parabola is the same distance from its focus and its axis. False. Every point on a parabola is equidistant from its focus and its directrix, a line perpendicular to the axis.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 18 Homework, Page 641 69.The focus of y 2 = 12x is a.(3, 3) b.(3, 0) c.(0, 3) d.(0, 0) e.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 19 What you’ll learn about Geometry of an Ellipse Translations of Ellipses Orbits and Eccentricity Reflective Property of an Ellipse … and why Ellipses are the paths of planets and comets around the Sun, or of moons around planets.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 20 Ellipse An ellipse is the set of all points in a plane whose distance from two fixed points in the plane have a constant sum. The fixed points are the foci (plural of focus) of the ellipse. The line through the foci is the focal axis. The point on the focal axis midway between the foci is the center. The points where the ellipse intersects its axis are the vertices of the ellipse.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 21 Key Points on the Focal Axis of an Ellipse

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 22 Ellipse - Additional Terms The major axis is the chord connecting the vertices of the ellipse. The semimajor axis is the distance from the center of the ellipse and to one of the vertices. The minor axis is the chord perpendicular to the major axis and passing through the center of the ellipse. The semiminor axis is the distance from the center of the ellipse to one end of the minor axis, sometimes called a minor vertex.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 23 Ellipse with Center (0,0)

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

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 25 Example Finding the Vertices and Foci of an Ellipse

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 26 Example Finding an Equation of an Ellipse

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 27 Ellipse with Center (h,k)

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 28 Ellipse with Center (h,k)

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 29 Example Locating Key Points of an Ellipse

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 30 Example Finding the Equation of an Ellipse

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 31 Example Graphing an Ellipse Using Parametric Equations

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 32 Example Proving an Ellipse

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 33 Elliptical Orbits Around the Sun

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

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 35 Homework Homework Assignment #17 Review Section 8.2 Page 653, Exercises: 1 – 69 (EOO)

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

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 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 astronomy, optics, and navigation.

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

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 41 Hyperbola

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 42 Hyperbola

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 43 Hyperbola with Center (0,0)

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 44 Hyperbola Centered at (0,0)

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 45 Example Finding the Vertices and Foci of a Hyperbola

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 46 Example Sketching a Hyperbola by Hand

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 47 Example Finding an Equation of a Hyperbola

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 48 Hyperbola with Center (h,k)

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 49 Hyperbola with Center (h,k)

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 50 Example Locating Key Points of a Hyperbola

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 51 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?

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 52 Example Locating a Point Using Hyperbolas

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 53 Eccentricity of a Hyperbola