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I have no idea where to start so I found out what a lemniscate is.. but this didn't help me much. I have rearranged the equation for a:

a = sqrt ( (x^2 + y^2)^2 / 2(x^2 - y^2) )

a = x^2 + y^2 / sqrt (2(x^2 - y^2))

How do I proceed from here?