9. g

11. h

13. d

15. b

17. Vertices: (1, 0) and $(-1,0);$ foci: $(\sqrt{5},0)$ and $1(-\sqrt{5},0);$ transverse axis: x-axis; the hyperbola opens left and right; vertices of the fundamental rectangle: $(1,2),(-1,2),(-1,-2),(1,-2);$ asymptotes: $y=\pm 2x$

19. Vertices: (1, 1) and $(0,-1);$ foci: $(0,\sqrt{2})$ and $(0,-\sqrt{2});$ transverse axis: y-axis; the hyperbola opens up and down; vertices of the fundamental rectangle: $(1,1),(-1,1),(-1,-1),(1,-1);$ asymptotes: $y=\pm x$

21. Vertices: (0, 2) and $(0,-2);$ foci: $(0,2\sqrt{10})$ and $(0,-2\sqrt{10});$ transverse axis: y-axis; the hyperbola opens up and down; vertices of the fundamental rectangle: (6, 2) $(-6,2),(-6,-2),(6,-2);$ asymptotes: $y=\pm {\displaystyle \frac{1}{3}}x$

23. Vertices: (3, 0) and $(-3,0);$ foci: $(\sqrt{13},0)$ and $(-\sqrt{13},0);$ transverse axis: x-axis; the hyperbola opens left and right; vertices of the fundamental rectangle: $(3,2),(-3,2),(-3,-2),(3,-2);$ asymptotes: $y=\pm {\displaystyle \frac{2}{3}}x$

25. Vertices: (0, 1) and $(0,-1);$ foci: $(0,{\displaystyle \frac{\sqrt{5}}{2}})$ and $(0,-{\displaystyle \frac{\sqrt{5}}{2}});$ transverse axis: y-axis; the hyperbola opens up and down; vertices of the fundamental rectangle: $({\displaystyle \frac{1}{2}},1),(-{\displaystyle \frac{1}{2}},1),(-{\displaystyle \frac{1}{2}},-1),({\displaystyle \frac{1}{2}},-1);$ asymptotes: $y=\pm 2x$

27. Vertices: $({\displaystyle \frac{1}{3}},0)$ and $(-{\displaystyle \frac{1}{3}},0);$ foci: $({\displaystyle \frac{\sqrt{10}}{3}},0)$ and $(-{\displaystyle \frac{\sqrt{10}}{3}},0);$ transverse axis: x-axis; the hyperbola opens left and right; vertices of the fundamental rectangle: $({\displaystyle \frac{1}{3}},1),(-{\displaystyle \frac{1}{3}},1),(-{\displaystyle \frac{1}{3}},-1),({\displaystyle \frac{1}{3}},-1);$ asymptotes: $y=\pm 3x$

29. ${\displaystyle \frac{x^2}{4}}-{\displaystyle \frac{y^2}{5}}=1$

31. ${\displaystyle \frac{y^2}{16}}-{\displaystyle \frac{x^2}{20}}=1$

33. ${\displaystyle \frac{y^2}{4}}-{\displaystyle \frac{x^2}{21}}=1$

35. $x^2-{\displaystyle \frac{y^2}{24}}=1$

37. ${\displaystyle \frac{y^2}{9}}-{\displaystyle \frac{x^2}{16}}=1$

39. $x^2-{\displaystyle \frac{y^2}{4}}=1$

41. ${\displaystyle \frac{y^2}{16}}-{\displaystyle \frac{x^2}{16}}=1$

43. Center: $(1,-1);$ vertices: $(4,-1)$ and $(-2,-1);$ transverse axis: $y=-1;$ asymptotes: $y+1=\pm {\displaystyle \frac{4}{3}}(x-1)$

45. Center: $(-2,0);$ vertices: (3, 0) and $(-7,0);$ transverse axis: x-axis; asymptotes: $y=\pm {\displaystyle \frac{7}{5}}(x+2)$

47. Center: $(-4,-3);$ vertices: $(1,-3)$ and $(-9,-3);$ transverse axis: $y=-3;$ asymptotes: $y+3=\pm {\displaystyle \frac{7}{5}}(x+4)$

49. Center: $(0,-1);$ vertices: $({\displaystyle \frac{5}{2}},-1)$ and $(-{\displaystyle \frac{5}{2}},-1);$ transverse axis: $y=-1;$ asymptotes: $y+1=\pm 2x$

51. Center: $(2,-1);$ vertices: (2, 4) and $(2,-6);$ transverse axis: $x=2;$ asymptotes:

53. Center: $(-3,0);$ vertices: $(-3+3\sqrt{5},0)$ and $(-3-3\sqrt{5},0);$ transverse axis: x-axis; asymptotes: $y=\pm (x+3)$

55. Center: $(-2,0);$ vertices: (2, 0) and $(-6,0);$ transverse axis: x-axis; asymptotes: $y=\pm {\displaystyle \frac{1}{2}}(x+2)$

57. Center: $(-3,-4);$ vertices: $(-3,-3)$ and $(-3,-5);$ transverse axis: $x=-3;$ asymptotes: $y+4=\pm \sqrt{2}(x+3)$

59. Center: $(3,-2);$ vertices: $(3+\sqrt{6},-2)$ and $(3-\sqrt{6},-2);$ transverse axis: $y=-2;$ asymptotes: $y+2=\pm {\displaystyle \frac{\sqrt{6}}{2}}(x-3)$

61. Center: $(\sqrt{2},0);$ vertices: $(\sqrt{2}+\sqrt{2\sqrt{2}+1},0)$ and $(\sqrt{2}-\sqrt{2\sqrt{2}+1},0);$ transverse axis: x-axis; asymptotes: $y=\pm (x-\sqrt{2})$

63. Parabola

65. Hyperbola

67. Circle

69. Parabola

71.

73. ${\displaystyle \frac{y^2}{9}}-{\displaystyle \frac{x^2}{8}}=1$

75. ${\displaystyle \frac{{(x+2)}^2}{9}}-{\displaystyle \frac{{(y-1)}^2}{7}}=1$

77. ${\displaystyle \frac{{(x+1)}^2}{4}}-{\displaystyle \frac{4y^2}{25}}=1$