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Study Guides > College Algebra

Solutions

Solutions to Try Its

1. ellipse; e=13;x=2e=\frac{1}{3};x=-2 2. 3. r=11cosθr=\frac{1}{1-\cos \theta } 4. 48x+3x2y2=04 - 8x+3{x}^{2}-{y}^{2}=0

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=1e=1 and directrix 34\frac{3}{4} units below the pole. 9. Hyperbola with e=2e=2 and directrix 52\frac{5}{2} units above the pole. 11. Parabola with e=1e=1 and directrix 310\frac{3}{10} units to the right of the pole. 13. Ellipse with e=27e=\frac{2}{7} and directrix 22 units to the right of the pole. 15. Hyperbola with e=53e=\frac{5}{3} and directrix 115\frac{11}{5} units above the pole. 17. Hyperbola with e=87e=\frac{8}{7} and directrix 78\frac{7}{8} units to the right of the pole. 19. 25x2+16y212y4=025{x}^{2}+16{y}^{2}-12y - 4=0 21. 21x24y230x+9=021{x}^{2}-4{y}^{2}-30x+9=0 23. 64y2=48x+964{y}^{2}=48x+9 25. 96y225x2+110y+25=096{y}^{2}-25{x}^{2}+110y+25=0 27. 3x2+4y22x1=03{x}^{2}+4{y}^{2}-2x - 1=0 29. 5x2+9y224x36=05{x}^{2}+9{y}^{2}-24x - 36=0 31. 33. 35. 37. 39. 41. 43. r=45+cosθr=\frac{4}{5+\cos \theta } 45. r=41+2sinθr=\frac{4}{1+2\sin \theta } 47. r=11+cosθr=\frac{1}{1+\cos \theta } 49. r=7828cosθr=\frac{7}{8 - 28\cos \theta } 51. r=122+3sinθr=\frac{12}{2+3\sin \theta } 53. r=1543cosθr=\frac{15}{4 - 3\cos \theta } 55. r=333cosθr=\frac{3}{3 - 3\cos \theta } 57. r=±21+sinθcosθr=\pm \frac{2}{\sqrt{1+\sin \theta \cos \theta }} 59. r=±24cosθ+3sinθr=\pm \frac{2}{4\cos \theta +3\sin \theta }

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