Parabola
A simple parabola with its axis of symmetry parallel to the y-axis with the vertex at (0,0) is:
and the focus of that parabola is at:
So, for a parabola such as y=x², with the a coefficient 1, the focus f is (0,¼).
Different parabolas with the same focus.
Table of x and ys with P (the focus aka f) set to 10. Note the European comma is the US period.
Diagram of x and ys with P (the focus aka f) set to 10. Note the European comma is the US period.
Tool for drawing parabolas.
Parabolic basket and tin can solar cooker team drawing out a parabola.
The main mathematical labels of a parabola.
[edit] Parabola technologies
Parabolas can be used for many things, for example solar cookers, solar turbines and antennas or waveguides for wireless transmission.
In these cases, some medium, for example sunlight or electromagnetic radiation, is being focused by the parabola. A single parabolic arc will create a focal line, whereas an elliptic paraboloid will create a single focus point. An alternative to paraboloids is to use two parabolas at 90° angles to each other, where one gathers the medium into a line and the other condenses the resulting line into a point. This is often easier to achieve with simple tools, but at a loss in efficiency. See Using Two Parabolic Troughs to Simulate a Paraboloid.
Parabolic solar cookers collect sunlight at the focus point, where it heats up and can be used for cooking. Similar parabolas are used to boil water in pipes (along a line) or in silos (at a focus point) to drive solar turbines (for boundary layer turbines it may be possible to use superheated air rather than water).
As antennas or waveguides, parabolas and paraboloids are highly directional. The FabFi project is an example of a system that uses paraboloid waveguides for directional wireless transmission.
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