Abstract
This chapter discusses paraboloids defined by ax2 + by2 + 2rz = 0. If the product abr ≠ 0, the paraboloid is nondegenerate. The degenerate cases are: (1) parabolic cylinder: a = 0 or b = 0, (2) pair of intersecting planes: r = 0, (3) pair of coincident planes: a = r = 0 or b = r = 0. Equation ax2 + by2 + 2rz = 0 contains even powers of x and y but not of z. Thus, a paraboloid is only symmetric in regard to the planes x = 0 and y = 0. There is no center in the usual sense and the origin is called the vertex, while the z-axis is called the axis. The chapter also discusses generators of hyperbolic paraboloid, center of a section, and axes of plane section.
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