The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).
Lemniscate Inverse Curve
See also
Rectangular HyperbolaExplore with Wolfram|Alpha
References
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 209, 1991.Referenced on Wolfram|Alpha
Lemniscate Inverse CurveCite this as:
Weisstein, Eric W. "Lemniscate Inverse Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemniscateInverseCurve.html