The Folium of Descartes

Introduction:

The well-known folium of Descartes can be defined parametrically or implicitly (see below). It has an asymptote with the equation y = -x - 1.

Definition:

Implicitly, the folium of Descartes is defined by

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: