1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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


    User Avatar
    Homework Helper

    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


    User Avatar
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    … 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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook