The Bullet Nose

Introduction:

The bullet nose is so named because the shape of its top or bottom half resembles a bullet. It is defined by replacing the exponent 2 in the equation for a hyperbola by a -2, as in the implicit equation below. Its parameterization is remarkably simple, but its arclength and curvature are still remarkably complicated.

Definition:

Implicitly, the curve is defined by

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: