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Parametric Transformations

  1. Apr 3, 2005 #1
    Okay, is it possible to transform an "x-y" equation into a parametric "equation"? If so, how would I go about it? For example, if I am given the equation (x^2)/1-(y^2)/25=1, what process would I have to use to find the Parametric equations?

    Thank You.
     
  2. jcsd
  3. Apr 3, 2005 #2
    If either variable was a function of the other, you could do the trivial way of letting one variable be the parameter. In any other case, there is no general way for generating a parametrization other than experience.
    For example, knowing the identity cosh2(t) - sinh2(t) = 1 shows us that one parametrization of the curve is x = cosh(t), y=5*sinh(t). The similarity to a certain parametrization of an ellipse makes their names as "hyperbolic" neighbors to sine and cosine clear.
     
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