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 Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0. These surfaces include familiar shapes such as spheres, ellipsoids, hyperboloids, and paraboloids, each characterized by specific coefficients in the equation. These surfaces can be classified based on their geometric properties and the signs of the coefficients. For example, a sphere is a special case of an ellipsoid where all axes are equal, while a hyperboloid can be one-sheeted or two-sheeted depending on its structure. Understanding quadric surfaces is essential in fields like geometry, computer graphics, and engineering.