1.

Vertex: (0, 0); focus: $(-{\displaystyle \frac{3}{2}},0)$; axis: x-axis; directrix: $x={\displaystyle \frac{3}{2}}$

3.

Vertex: (0, 0); focus: $(0,{\displaystyle \frac{7}{4}})$; axis: y-axis; directrix: $y=-{\displaystyle \frac{7}{4}}$

5.

Vertex: $(2,-3);$ focus: $(2,-{\displaystyle \frac{13}{4}})$; axis: $x=2$; directrix: $y=-{\displaystyle \frac{11}{4}}$

7.

Vertex: $(-{\displaystyle \frac{5}{2}},-2);$ focus: $(-2,-2);$ axis: $y=-2;$ directrix: $x=-3$

9. $y^2=-12x$

11. $x^2=16y$

13.

Foci: $(\sqrt{21},0)$ and $(-\sqrt{21},0);$ vertices: (5, 0) and $(-5,0)$; endpoints of the minor axis: (0, 2) and $(0,-2)$

15.

Foci: $(0,\sqrt{3})$ and $(0,-\sqrt{3});$ vertices: (0, 2) and $(0,-2)$; endpoints of the minor axis: (1, 0) and $(-1,0)$

17.

Foci: $(-1,-4+\sqrt{7})$ and $(-1,-4-\sqrt{7});$ vertices: $(-1,0)$ and $(-1,-8)$; endpoints of the minor axis: $(2,-4)$ and $(-4,-4)$

19.

Foci: $(-1+2\sqrt{2},1)$ and $(-1-2\sqrt{2},1);$ vertices: (2, 1) and $(-4,1)$; endpoints of the minor axis: $(-1,2)$ and $(-1,0)$

21. ${\displaystyle \frac{x^2}{16}}+{\displaystyle \frac{y^2}{4}}=1$

23. ${\displaystyle \frac{x^2}{100}}+{\displaystyle \frac{y^2}{75}}=1$

25.

Vertices: (0, 4) and $(0,-4);$ foci: $(0,2\sqrt{5})$ and $(0,-2\sqrt{5});$ asymptotes: $y=\pm 2x$

27.

Vertices: (1, 0) and $(-1,0);$ foci: (3, 0) and $(-3,0)$ asymptotes: $y=\pm 2\sqrt{2}x$

29.

Vertices: (1, 3) and $(-5,3);$ foci: $(-2+\sqrt{13},3)$ and $(-2-\sqrt{13},3);$ asymptotes: $y-3=\pm {\displaystyle \frac{2}{3}}(x+2)$

31.

Vertices: $(-2,-2)$ and $(-2,-8);$ foci: $(-2,-5+3\sqrt{5})$ and $(-2,-5-3\sqrt{5});$ asymptotes: $y+5=\pm {\displaystyle \frac{1}{2}}(x+2)$

33. $x^2-{\displaystyle \frac{y^2}{3}}=1$

35. ${\displaystyle \frac{x^2}{4}}-{\displaystyle \frac{y^2}{36}}=1$

37. Hyperbola

39. Ellipse

41. Circle

43. Hyperbola

45. Circle

47. Ellipse

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

51. Point of intersection:

$({\displaystyle \frac{109}{10}},-{\displaystyle \frac{91}{20}})$

53. Points of intersection: $(2,1),(2,-1),(-2,1),(-2,-1)$

55. 14.6 ft

57. 16.4 in.