A hyperbolic spiral is a transcendental

Transcendental function

A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation...

 plane curve

Plane curve

In mathematics, a plane curve is a curve in a Euclidean plane . The most frequently studied cases are smooth plane curves , and algebraic plane curves....

 also known as a reciprocal spiral. A hyperbolic spiral is the opposite of an Archimedean spiral

Archimedean spiral

The Archimedean spiral is a spiral named after the 3rd century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity...

 and are a type of Cotes' spiral.
It has the polar equation:

It begins at an infinite distance from the pole in the centre (for θ starting from zero r = a/θ starts from infinity), it winds faster and faster around as it approaches the pole, the distance from any point to the pole, following the curve, is infinite.