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