THE FUNDAMENTAL PROPERTIES OF ELLIPSOIDS, HYPERBOLOIDS, AND PARABOLOIDS

Boboqulova Durdona Sanjar qizi

First-year student of the Mathematics Department, Faculty of Pedagogy, Shahrisabz State Pedagogical Institute

Keywords: Keywords: quadric surfaces, ellipsoid, hyperboloid, paraboloid, 3D geometry, surface curvature, conic sections.

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Abstract

Abstract: This paper explores three primary types of second-order (quadric) surfaces: the ellipsoid, the hyperboloid, and the paraboloid. These surfaces play a central role in 3D geometry, engineering modeling, physics, and computer graphics. We analyze their standard equations, geometric interpretations, and key properties, including symmetry, curvature, and cross-sectional behavior. Their classification within the broader family of quadratic surfaces is also presented with visual and algebraic insight.

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References

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