The Parabola

Introduction:

The parabola is a well-known conic section, formed by slicing a cone with a plane that is parallel to one of the cone's edges.

Definition:

Geometrically, the parabola is defined by two objects: a point (called the focus) and a line (called the directrix). The parabola is the set of all points at an equal distance from the point and the line (dropping a perpendicular). In the parameterization above, the focus is at (0, a) and the directrix is the line y = -a.

Properties:

Velocity and Acceleration:

The Tangent Vector:

Arc Length:

Curvature: