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Subject: calculate a parabola from 5 diff points


Author:
guy
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Date Posted: 02:07:44 05/26/04 Wed

hi i need some help im trying to find an algorithm for
finding the equation of a parabola from 5 diff points
thanks for your time!!!
guy

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[> Subject: Re: calculate a parabola from 5 diff points


Author:
QUITTNER
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Date Posted: 10:19:03 05/27/04 Thu

>>> hi i need some help im trying to find an algorithm for finding the equation of a parabola from 5 diff points thanks for your time!!! guy <<<
..... A parabola is fully described by only 3 points. If you are given more than 3 points then you could use "the least squares method" to find the closest approximate parabola, meaning finding a parabola whose value at a given x, call it y, is a distance, call it d, away from a given point at that x, with the sum of all the (d squared) being at a minimum. Is that what you want?

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[> [> Subject: Re: calculate a parabola from 5 diff points


Author:
QUITTNER
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Date Posted: 11:36:38 06/17/04 Thu

By the way, some people use A+Bx+Cx^2 as a general equation of what they call a parabola.
..... A REAL parabola is NOT the same as that, but is defined as a curve, all of whose points are at the SAME distance from a given line and from a given point, called the "Focal Point". The equation of a special kind of parabola is (y-A)^2=K*(x-B), with, in an even more special case, A and B are both zero.
..... If there are 3 unknowns then you need 3 simultaneous equations to solve (can be quite dificult!) for these unknowns.

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