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Math Help - Conics- Rotating The Axis

  1. #1
    Newbie BishBashBosh's Avatar
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    Conics- Rotating The Axis

    If the form of a conic is

    ax˛ + 2hxy + by˛ + 2fx + 2gy + k = 0

    and to rotate the axis from (x,y) to (X,Y) you must use

    x = XcosT - YsinT
    y = XsinT + YcosT

    how can I show that to get rid of the xy coefficient, T must be found using

    tan(2T) = 2h / (a-b)???
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  2. #2
    Flow Master
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    Quote Originally Posted by BishBashBosh View Post
    If the form of a conic is

    ax˛ + 2hxy + by˛ + 2fx + 2gy + k = 0

    and to rotate the axis from (x,y) to (X,Y) you must use

    x = XcosT - YsinT
    y = XsinT + YcosT

    how can I show that to get rid of the xy coefficient, T must be found using

    tan(2T) = 2h / (a-b)???
    NationMaster - Encyclopedia: Rotation of Axes
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