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Find and verify parametric equations for an ellipse

  • Thread starter the.flea
  • Start date
  • #1
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1. Homework Statement
Find and verify parametric equations for an ellipse.


2. Homework 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?
 

Answers and Replies

  • #2
dynamicsolo
Homework Helper
1,648
4
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.
 
  • #3
23
0
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.
 
  • #4
23
0
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.
 
  • #5
dynamicsolo
Homework Helper
1,648
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.
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.
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,789
249
… just plug'n'play …

x=acost
y=bsint

x2 y2
-- + -- = 1
a2 b2
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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