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Area and Centroid
Area and Centroid
A parabola is the locus (position) of points in that plane that are equidistant from both the directrix and the focus.
Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface
The focus of a parabola at distance a from its vertex and is given by:
The area of parabolic segment is:
The location of the centroid from the base is:
Semiparabola and spandrel of parabola
Semiparabola and spandrel of parabola
For semiparabolic segment:
For spandrel of parabola:
General spandrel
General spandrel
For the general spandrel shown:
The moment of inertia about the x- and y-axes is:
Length of parabolic arc
Length of parabolic arc
In general, the length of a parabolic arc from point 1 to point 2 is:
The total length of the parabolic arc shown may be calculated by:
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