1.
Vertex: (0, 0); focus: (−32, 0); axis: x-axis; directrix: x=32
3.
Vertex: (0, 0); focus: (0, 74); axis: y-axis; directrix: y=−74
5.
Vertex: (2,−3); focus: (2,−134); axis: x=2; directrix: y=−114
7.
Vertex: (−52,−2); focus: (−2,−2); axis: y=−2; directrix: x=−3
9. y2=−12x
11. x2=16y
13.
Foci: (21−−√, 0) and (−21−−√, 0); vertices: (5, 0) and (−5, 0); endpoints of the minor axis: (0, 2) and (0,−2)
15.
Foci: (0, 3–√) and (0,−3–√); vertices: (0, 2) and (0,−2); endpoints of the minor axis: (1, 0) and (−1, 0)
17.
Foci: (−1,−4+7–√) and (−1,−4−7–√); vertices: (−1, 0) and (−1,−8); endpoints of the minor axis: (2,−4) and (−4,−4)
19.
Foci: (−1+22–√, 1) and (−1−22–√, 1); vertices: (2, 1) and (−4, 1); endpoints of the minor axis: (−1, 2) and (−1, 0)
21. x216+y24=1
23. x2100+y275=1
25.
Vertices: (0, 4) and (0,−4); foci: (0, 25–√) and (0,−25–√); asymptotes: y=±2x
27.
Vertices: (1, 0) and (−1, 0); foci: (3, 0) and (−3, 0) asymptotes: y=±22–√x
29.
Vertices: (1, 3) and (−5, 3); foci: (−2+13−−√, 3) and (−2−13−−√, 3); asymptotes: y−3=±23(x+2)
31.
Vertices: (−2,−2) and (−2,−8); foci: (−2,−5+35–√) and (−2,−5−35–√); asymptotes: y+5=±12(x+2)
33. x2− y23=1
35. x24− y236=1
37. Hyperbola
39. Ellipse
41. Circle
43. Hyperbola
45. Circle
47. Ellipse
49. x25−y24=1
51. Point of intersection:
(10910,−9120)
53. Points of intersection: (2, 1), (2,−1), (−2, 1), (−2,−1)
55. 14.6 ft
57. 16.4 in.