Elliptic cylinder
If AB > 0 this is the equation of an elliptic cylinder.[15] Further simplification can be obtained by translation of axes and scalar multiplication. If has the same sign as the coefficients A and B, then the equation of an elliptic cylinder may be rewritten in Cartesian coordinates as:
This equation of an elliptic cylinder is a generalization of the equation of the ordinary, circular cylinder (a = b). Elliptic cylinders are also known as cylindroids, but that name is ambiguous, as it can also refer to the Plücker conoid.
Parabolic cylinder[edit]
Finally, if AB = 0 assume, without loss of generality, that B = 0 and A = 1 to obtain the parabolic cylinders with equations that can be written as:[16]
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