ELLIPTIC PARABOLOID 
elliptic paraboloid
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=2cz\) Real plane intersections: the ellipses, the circles and the parabolas. 
paraboloid of revolution \(\frac{x^2}{a^2}+\frac{y^2}{a^2}=2cz\) It is obtained by rotating a parabola about its axis. Real plane intersections: the ellipses, the circles and the parabolas. 
HYPERBOLIC PARABOLOID 
\(\frac{x^2}{a^2}\frac{y^2}{b^2}=2cz\)
Doubly ruled surface  through every point on the surfaces there are two lines on the surfaces, two systems of rulings. Real plane intersections are: the parabolas, the hyperbolas and degenerated conics  pairs of real lines (intersection with the tangent planes). 

Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja  3DGeomTeh  Developing project of the University of Zagreb