Parabola

A Parabola is a Conic Section and describes the path (or trajectory) taken by a ball as it is thrown in the air.

An important characteristic of a parabola-shaped reflector is that any beam of light, sound or other energy which enters travelling parallel to its main axis is reflected through a single point called its focus. Conversely, light that originates from a point source at the focus is reflected into a parallel beam. This makes parabolic forms (i.e. parabloids) very useful for microphones and spotlight reflectors for example.

Parabolas can be drawn as the graph of y=x² but there are other ways of drawing a parabola which exploit its various mathematical properties.

Using measured Abscissae

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A property of the parabola is that the abscissa, that part of a diameter of a conic between its vertex and an ordinate, is proportional to the product of the parts into which it divides the double ordinate. So, start by drawing a horizontal ordinate, say 4 units long, then doubling it to become a line 8 units long, Number equi-spaced divisions on the double ordinate, say 0 to 8, and back again as shown. Set the height of the parabola vertex as required, and divide this into the same number of units as the ordinate (i.e. 4 in this example). The height of each Abscissa is given in vertically scaled units as the products of the two numbers that result - i.e. 0x8, 1x7, 2x6, 3x5, etc.

File:Parabola1.jpg