Math Is Fun Forum

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.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,427

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

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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.