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#1 2005-11-25 10:49:16

Zoid
Member
Registered: 2005-11-25
Posts: 2

Lemniscate in Parametric Form

Hi,

I'm working on a report in which I have to take the definition of a lemniscate and use it to develop a system of parametric equations to describe it. I know that the most common such system is x = (a * cos t)/(1+sin^2 t) and y = (a * sin t cos t)/(1+sin^2 t).

My question is... how do you derive this from the definition of a lemniscate?

Thanks in advance for any help.

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#2 2005-11-25 16:27:38

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

Re: Lemniscate in Parametric Form

A lemniscate is a curve with the cartesian equation
(x²  + y²)²  = a² (x²  - y²)
It is like this :- ∞
The polar equation is
r²=a²Cos2θ

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2005-11-26 07:52:02

Zoid
Member
Registered: 2005-11-25
Posts: 2

Re: Lemniscate in Parametric Form

Thank you.

But I still don't understand where x = (a * cos t)/(1+sin^2 t) and y = (a * sin t cos t)/(1+sin^2 t) come from.

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