Quadric surfaces are a type of three-dimensional geometric shape defined by a second-degree polynomial equation in three variables, typically written in the form Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz = 0. These surfaces include familiar shapes such as ellipsoids, hyperboloids, and paraboloids, each characterized by specific coefficients and terms in the equation. These surfaces can be classified based on their properties and the signs of the coefficients. For example, an ellipsoid has all positive coefficients, while a hyperboloid has both positive and negative coefficients. Understanding quadric surfaces is essential in fields like geometry, engineering, and computer graphics.