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Find and verify parametric equations for an ellipse

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Find and verify parametric equations for an ellipse.


    2. Relevant equations
    x=acost
    y=bsint

    3. The attempt at a solution

    lets say the equation is x=3cost, y=3sint, domain: 0 to 2pi

    x2 y2
    -- + -- = 1
    a2 b2

    point does verify when t=0 x=3, y=0 which =1
    any help?
     
  2. jcsd
  3. Mar 23, 2008 #2

    dynamicsolo

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    Are you asking about the conversion of the equation for the ellipse from rectangular (Cartesian) to polar coordinates? You already have the first step: your parameterization is actually using polar coordinates, where the angle [tex]\theta[/tex] is expressed as a function of time t (in the simplest possible way, [tex]\theta = t[/tex] ).

    If you substitute your expressions for x and y into the rectangular form of the equation, some work with trig identities will get you to a polar form.
     
  4. Mar 23, 2008 #3
    I'm sorry I do not understand. Please simplify the sentence.
    There is a question asking to find and verify parametric equations for an ellipse. How would we start and finish such a complex question? Thank you in advance.
     
  5. Mar 23, 2008 #4
    I think I understand most of what you are saying, however I am not trying to go from rectangular to polar, I just want to verify this in rectangular form.
     
  6. Mar 23, 2008 #5

    dynamicsolo

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    I took back my last posting because I wasn't sure what you were asking for. If the problem is just asking for verification of the parametrization, you can just substitute the expressions for x and y into the equation for the ellipse. What do you get? If the statement you arrive at is always true, you have verified the parametrization you were given.

    What I was wondering is whether they wanted you to use the polar equation

    r^2 = x^2 + y^2

    and simplify the result into a function r = r(t). But maybe that's more than they're looking for.
     
  7. Mar 23, 2008 #6

    tiny-tim

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    … just plug'n'play …

    Hi, tiny flea! :smile:

    If you're supposed to prove that x=acost, y=bsint satisfies x2/a2 + y2/b2 = 1, why don't you just plug those parametric values for x and y into the equation, and confirm that it is correct?

    What is worrying you about that? :smile:
     
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