Find and verify parametric equations for an ellipse

[the.flea]

Homework Statement

Find and verify parametric equations for an ellipse.

Homework Equations

x=acost
y=bsint

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?

 

[dynamicsolo]

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 $$\theta$$ is expressed as a function of time t (in the simplest possible way, $$\theta = t$$ ).

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.

 

[the.flea]

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.

 

[the.flea]

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.

 

[dynamicsolo]

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.

 

[tiny-tim]

… just plug'n'play …

x=acost
y=bsint

x2 y2
-- + -- = 1
a2 b2

Hi, tiny flea!

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?