Finding the Angle of Rotation

Key Questions

  • What is does an #xy# term indicate in the equation for a conic section?

    xy term in the equation of a conic section indicates, there is a rotation of axes

    bp · 2 · Jul 22 2015
  • How do I find the angle of rotation of a hyperbola?

    Answer:

    Use a formula and solve for angle of rotation = #theta#

    Explanation:

    For the formulas I use, we must put the equation in the form:

    #Ax^2 +Bxy+Cy^2 +Dx + Ey +F =0#

    Use #cot2theta = (A-C)/B# or #tan2theta = B/(A-C)#.

    Solve for #theta#.

    (The #D, E, " and " F# are not used in the formulas.)

    Your textbook/teacher may prefer a different form, which would lead to different formulas.

    Note/Example:
    If #A = C#, then #cot2theta = 0#, so #theta = pi/4#

    Jim H · 1 · Jul 9 2015

Questions

Translation and Rotation of Axis