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Equation general of conic in polar coordinates

  1. Jun 14, 2014 #1
    The conic equation has 2 versions in cartesian coordinates:

    The general: ##Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0##
    And the parametric: ##y^2 = 2px + (e^2-1)x^2##

    In polar coordinates, I known just the parametric: ##r = \frac{p}{1+e\cos(\theta)}##
    But exist a general form too?
     
  2. jcsd
  3. Jun 14, 2014 #2

    mfb

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    You can express x and y in your general equation in terms of r and θ to get the general form. I think it will look quite messy. The parametric uses the "right" coordinate system, where the equation has a nice form. Usually there is no point in polar coordinates if the center does not have a special meaning.
     
  4. Jun 19, 2014 #3
    But what you are suggesting is a transformation... I'm not looking for this, but yes by a general expression/format that is a conic but is independent of the cartesian format...
     
  5. Jun 19, 2014 #4

    mfb

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    Well, you look for the result of a transformation. Isn't it natural to just do this transformation then?
     
  6. Jun 19, 2014 #5
    Ahhh, does not matter... thanks of anyway
     
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