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The parabola is a member of the family of conic sections. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
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It has been proved that the Kiepert hyperbola is the hyperbola passing through the vertices, the centroid and the orthocenter of the reference triangle and the Kiepert parabola is the parabola inscribed in the reference triangle having the Euler line as directrix and the triangle center X 110 as focus. [1]
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
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A parabola, showing arbitrary line (L), focus (F), and vertex (V). Generic points marked for explanation. Adapted from this image, which shows L as the directrix of ...
Parabola-and-inscribed_triangle.png: Mattes This is a retouched picture , which means that it has been digitally altered from its original version. Modifications: Converted image to SVG .
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