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Mathematics LibreTexts

12.5E: Conic Sections in Polar Coordinates (Exercises)

  • Page ID
    56135
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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.