Parabola modeling

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How do I create a parabola (datum curve) when I know the focal point?

 

[kvision]

The definition of a parabola is that the distance from the focal point to any point on the curve is equal to the distance from the point on the curve to the directrix which is a line parallel to the x axis and is 2*a from the focal point if a is the focal length. Do the math. y+a = sqrt((x-0)^2+(y-a)^2) which reduces to y=x^2/(4*a).

use this in an equation to create the curve. as an example a parabola with a focal length of .25 and centered on the y axis opening upward can be done with the following equations.

a=.25 (focal length)

x=2*t-1 (x goes from -1 to 1)

y=x^2/(4*a) (parabola in x-y plane)

z=0 (is in x-y plane)

good luck.

 

[kvision]

heres a screen shot of the parabola with a description of the setup.

http://www.kinetivision.com/images/request/parabola.gif