1012 CHAPTER 10 Analytic Geometry Graph each equation. Give the domain and range. Identify any that are functions. See Example 3. 33. y 2 = B1 - x2 25 34. x 4 = B1 - y2 9 35. x = - B1 - y2 64 36. y = - B1 - x2 100 Determine the two equations necessary to graph each ellipse using a graphing calculator, and graph it in the viewing window indicated. See Figure 18. 37. x2 16 + y2 4 = 1; 3-6.6, 6.64 by 3-4.1, 4.14 38. x2 4 + y2 25 = 1; 3-6.6, 6.64 by 3-5.2, 5.24 39. 1x - 322 25 + y2 9 = 1; 3-9.9, 9.94 by 3-8.2, 8.24 40. x2 36 + 1y + 422 4 = 1; 3-9.9, 9.94 by 3-8.2, 8.24 Write the equation of each ellipse in standard form. Give the center, vertices, and endpoints of the minor axis. See Example 5. 41. 4x2 + 8x + 25y2 - 250y = -529 42. 9x2 + 72x + 16y2 - 128y = -256 43. 49x2 + 9y2 + 108y - 117 = 0 44. 4x2 - 24x + y2 + 20 = 0 45. x2 + 12y2 - 14x - 48y + 85 = 0 46. 10x2 + y2 + 120x + 2y + 351 = 0 47. 4x2 + 3y2 - 72x + 36y = -408 48. 5x2 + 7y2 + 80x - 140y = -985 Find the eccentricity e of each ellipse. Round to the nearest hundredth as needed. See Example 6. 49. x2 3 + y2 4 = 1 50. x2 8 + y2 4 = 1 51. 4x2 + 7y2 = 28 52. x2 + 25y2 = 25 53. Concept Check Draftspeople often use the method shown in the sketch to draw an ellipse. Why does this method work? 54. Concept Check How can the method of Exercise 53 be modified to draw a circle? 28. foci at 1-3, -32, 17, -32; the point 12, -72 on ellipse 29. e = 4 5; vertices at 1-5, 02, 15, 02 30. e = 1 2; vertices at 1-4, 02, 14, 02 31. e = 3 4; foci at 10, -22, 10, 22 32. e = 2 3; foci at 10, -92, 10, 92 Solve each problem. See Examples 7 and 8. 55. Height of an Overpass A one-way road passes under an overpass in the shape of half an ellipse, 15 ft high at the center and 20 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass? 20 ft 15 ft NOT TO SCALE
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