elliptic paraboloid

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A quadric whose equation in a suitable coordinate system isHere the yz-plane and the zx-plane are planes of symmetry. Sections by planes z=k, where k≥0, are ellipses (circles if a=b); planes z=k, where k < 0, have no points of intersection with the paraboloid. Sections by planes parallel to the yz-plane and to the zx-plane are parabolas. Planes through the z-axis cut the paraboloid in parabolas with vertex at the origin.

Subjects: Mathematics.

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