THE FUNDAMENTAL PROPERTIES OF ELLIPSOIDS, HYPERBOLOIDS, AND PARABOLOIDS - Boboqulova Durdona Sanjar qizi (FANLARARO TAFAKKUR MAVZUSIDAGI ILMIY-AMALIY KONFERENSIYA, 2025)
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.