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SKEW (CUBICAL) PARABOLA
Name given by Seydewitz in 1847. 
System of Cartesian equations: .
Cartesian parametrization: . 
The skew (cubical) parabola is the curve with the above parametrization.
Its name comes from the fact that its projections on the planes xOy, xOz and yOz are a parabola, a cubical parabola, and a semicubical parabola. 

It is the intersection between three quadrics:
(parabolic cylinder), (hyperbolic paraboloid), and (cone of revolution). 
intersection of the cylinder and the paraboloid (that also share the line at infinity of the plane x = 0) 
intersection of the cylinder and the cone (that also share the line Oz) 
view of the 3 quadrics (Alain Esculier) 
Its projection on the plane y + z = 0 is, up to scaling, a Tschirnhausen cubic
(parametrization ). 
See also the tangent developable of the skew parabola.
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© Robert FERRÉOL 2018