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When , the solution is the hyperbolic spiral.
A hyperbolic spiral is a transcendental plane curve also known as a reciprocal spiral.
Other spirals falling into this group include the hyperbolic spiral, Fermat's spiral, and the lituus.
The hyperbolic spiral:
A hyperbolic spiral is the opposite of an Archimedean spiral and are a type of Cotes' spiral.
The first form corresponds to an epispiral, and the second to one of Poinsot's spirals; the third form corresponds to a hyperbolic spiral, also known as a reciprocal spiral, which is sometimes not counted as a Cotes's spiral.
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