Explore BrainMass

Explore BrainMass

    Conic Sections in Polar Coordinates

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (a)
    Also, we have (1)
    Pl is parallel to the x-axis, so Pl = DE (2)
    And (3)
    Substitute (2) and (3) to equation (1), we have
    Therefore,

    Then PF = r
    According to the definition of e, we have , so

    (*)

    The conversion between the polar and rectangular coordinates is
    (4)
    Therefore, (5)
    Square both sides of equation (*), we have
    (6)
    Substitute equations (4) and (5) to (6)

    (7)
    When e <1, , so , that is, the coefficient of is greater than 0. so it is an equation of ellipse.

    When e > 1, , equation (7) is
    , so it is an equation of hyperbola.

    © BrainMass Inc. brainmass.com June 3, 2020, 8:20 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/conic-sections-polar-coordinates-133116

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    4. The conversion between the polar and rectangular coordinates is
    (1)
    Therefore, (2)
    Given that:
    Cross-multiplying,
    r + r e cos = ed, or r = ...

    Solution Summary

    Conic Sections in Polar Coordinates are investigated.

    $2.19

    ADVERTISEMENT