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

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,759

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

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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