Elliptical paraboloid . It is the surface that has been created by sliding a vertical parabola with the concavity down, along the other, perpendicular to the first; horizontal sections are ellipses while vertical sections are parabolas.
Summary
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- 1 Definition
- 2 Features
- 3 Application
- 1 Curiosity
- 4 Sources
Definition
The surface that in a Cartesian coordinate system is determined by the equation is called Elliptical Paraboloid
The sections of which are parabolic or elliptical. The case of revolution is obtained by rotating a parabola around its axis of symmetry and it turns out to be the locus of the centers of the spheres that pass through a point and are tangent to a plane.
characteristics
Graph of an elliptical paraboloid
The point that coincides with the coordinate origin is called the vertex of the paraboloid. If the figure does not coincide with the origin of coordinates at the vertex, then the equation is:
The sections obtained by cutting the figure by planes with the Oz axis are parabolas. The sections obtained by cutting the figure by planes with the Oz axis are ellipses.
Paraboloid in Revolution
When a = b is the elliptical paraboloid it is a Paraboloid in Revolution.
Application
It has the shape of the so-called parabolic antennas, among other uses of daily origin. It has the property of reflecting (in case of having a reflecting surface) the light towards a point.
Curiosity
If you move a half-filled glass circularly, the surface that forms the upper part of the liquid is an Elliptical Hyperboloid.
