En la Geometría analítica, un paraboloide es una cuádrica, un tipo de superficie tridimensional que se describe mediante ecuaciones cuya forma canónica es del tipo: Los paraboloides pueden ser elípticos o hiperbólicos, según sea que sus términos cuadráticos (los que contienen variables elevadas al cuadrado, aquí indicadas como x e y) tengan igual o distinto signo, respectivamente.

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In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it can be represented by the equation where a and b are constants that dictate the level of curvature in the xz and yz planes respectively. This is an elliptic paraboloid which opens upward for c > 0 and downward for c < 0. The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a hyperbolic paraboloid can be represented by the equation For c > 0, this is a hyperbolic paraboloid that opens down along the x-axis and up along the y-axis (i.e., the parabola in the plane x = 0 opens upward and the parabola in the plane y=0 opens downward).

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