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:
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The Tangent Vector:
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Arc Length: |
Curvature:
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