Solutions to Odd-Numbered Exercises

1. If eccentricity is less than 1, it is an ellipse. If eccentricity is equal to 1, it is a parabola. If eccentricity is greater than 1, it is a hyperbola.

3. The directrix will be parallel to the polar axis.

5. One of the foci will be located at the origin.

7. Parabola with $e=1$ and directrix $\frac{3}{4}$ units below the pole.

9. Hyperbola with $e=2$ and directrix $\frac{5}{2}$ units above the pole.

11. Parabola with $e=1$ and directrix $\frac{3}{10}$ units to the right of the pole.

13. Ellipse with $e=\frac{2}{7}$ and directrix $2$ units to the right of the pole.

15. Hyperbola with $e=\frac{5}{3}$ and directrix $\frac{11}{5}$ units above the pole.

17. Hyperbola with $e=\frac{8}{7}$ and directrix $\frac{7}{8}$ units to the right of the pole.

19. $25{x}^{2}+16{y}^{2}-12y - 4=0$

21. $21{x}^{2}-4{y}^{2}-30x+9=0$

23. $64{y}^{2}=48x+9$

25. $96{y}^{2}-25{x}^{2}+110y+25=0$

27. $3{x}^{2}+4{y}^{2}-2x - 1=0$

29. $5{x}^{2}+9{y}^{2}-24x - 36=0$

31.

33.

35.

37.

39.

41.

43. $r=\frac{4}{5+\cos \theta }$

45. $r=\frac{4}{1+2\sin \theta }$

47. $r=\frac{1}{1+\cos \theta }$

49. $r=\frac{7}{8 - 28\cos \theta }$

51. $r=\frac{12}{2+3\sin \theta }$

53. $r=\frac{15}{4 - 3\cos \theta }$

55. $r=\frac{3}{3 - 3\cos \theta }$

57. $r=\pm \frac{2}{\sqrt{1+\sin \theta \cos \theta }}$

59. $r=\pm \frac{2}{4\cos \theta +3\sin \theta }$