quadric surface

A quadric surface is a three-dimensional surface defined by a second-order polynomial equation. In simpler terms, it's a surface described by an equation where the highest power of the variables (x, y, and z) is two.1

If the equation is in a simplified form like (ax^2 + by^2 + cz^2 = 1), the surface can be an ellipsoid (if a, b, and c are positive) or a hyperboloid (if one or two coefficients are negative). Other possibilities include cylinders, cones, and paraboloids, such as (z = x^2 + y^2) or (z = x^2 - y^2). Every point on a quadric surface has two straight lines passing through it that lie on the surface itself. The term "quadric" can also be used as an adjective meaning "quadratic," especially when referring to equations with more than two variables.12