Solutions

Solutions to Try Its

1. Focus: (−4,0); Directrix: x=4; Endpoints of the latus rectum: (−4,±8)

2. Focus: (0,2); Directrix: y=−2; Endpoints of the latus rectum: (±4,2).

3. x2=14y

4. x2=14y

5. Vertex: (8,−1); Axis of symmetry: y=−1; Focus: (9,−1); Directrix: x=7; Endpoints of the latus rectum: (9,−3) and (9,1).

6. Vertex: (−2,3); Axis of symmetry: x=−2; Focus: (−2,−2); Directrix: y=8; Endpoints of the latus rectum: (−12,−2) and (8,−2).

7.  a. y2=1280x
b. The depth of the cooker is 500 mm

Solutions to Odd-Numbered Exercises

1. A parabola is the set of points in the plane that lie equidistant from a fixed point, the focus, and a fixed line, the directrix.

3. The graph will open down.

5. The distance between the focus and directrix will increase.

7. yes y=4(1)x2

9. yes (y−3)2=4(2)(x−2)

11. y2=18x,V:(0,0);F:(132,0);d:x=−132

13. x2=−14y,V:(0,0);F:(0,−116);d:y=116

15. y2=136x,V:(0,0);F:(1144,0);d:x=−1144

17. (x−1)2=4(y−1),V:(1,1);F:(1,2);d:y=0

19. (y−4)2=2(x+3),V:(−3,4);F:(−52,4);d:x=−72

21. (x+4)2=24(y+1),V:(−4,−1);F:(−4,5);d:y=−7

23. (y−3)2=−12(x+1),V:(−1,3);F:(−4,3);d:x=2

25. (x−5)2=45(y+3),V:(5,−3);F:(5,−145);d:y=−165

27. (x−2)2=−2(y−5),V:(2,5);F:(2,92);d:y=112

29. (y−1)2=43(x−5),V:(5,1);F:(163,1);d:x=143

31. 

33.

35.

37.

39.

41.

43. 

45. x2=−16y

47. (y−2)2=42(x−2)

49. (y+3)2=−42(x−2)

51. x2=y

53. (y−2)2=14(x+2)

55. (y−3)2=45(x+2)

57. y2=−8x

59. (y+1)2=12(x+3)

61. (0,1)

63. At the point 2.25 feet above the vertex.

65. 0.5625 feet

67. x2=−125(y−20), height is 7.2 feet

69. 2304 feet