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# 12.5E: Conic Sections in Polar Coordinates (Exercises)

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For the following exercises, given the polar equation of the conic with focus at the origin, identify the eccentricity and directrix.

41. $$r=\frac{10}{1-5 \cos \theta}$$

42. $$r=\frac{6}{3+2 \cos \theta}$$

43. $$r=\frac{1}{4+3 \quad \sin \theta}$$

44. $$r=\frac{3}{5-5} \sin \theta$$

For the following exercises, graph the conic given in polar form. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse or a hyperbola, label the vertices and foci.

45. $$r=\frac{3}{1-\sin \theta}$$

46. $$r=\frac{8}{4+3} \sin \theta$$

47. $$r=\frac{10}{4+5 \cos \theta}$$

48. $$r=\frac{9}{3-6 \quad \cos \theta}$$

For the following exercises, given information about the graph of a conic with focus at the origin, find the equation in polar form.

49. Directrix is $$x=3$$ and eccentricity $$e=1$$

50. Directrix is $$y=-2$$ and eccentricity $$e=4$$

12.5E: Conic Sections in Polar Coordinates (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.