Paraboloids

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.
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\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=2cz\) 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