(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I understand that the general equation of a conic is:

And I know that I can use 5 points to determine the unique conic that passes through these points.

What I don't understand, however, is this site's explanation of the process:

http://home.att.net/~srschmitt/zenosamples/zs_conic_eqn_5points.html" [Broken]

The reason being is that, under the header of "Fitting a Conic Section Through Five Points,"

they declare that there is one and only one conic that may fit through these five points. However, they have to define the F variable before they solve the matrix. This seems contradictory to me. Why do they have to define F in order to pick a unique conic? Wouldn't F be defined already?

My overarching problem, however, is merely to find an ellipse based on a number of points. It is for a program that will predict the orbit of a controllable-planet by using past positions. Is there an easier way to find the length, width, position, and orientation of an ellipse?

Wolfram-Alpha's page on ellipses is very helpful in giving me a way to find those values if I have all the variables in the general equation, but is there an easier way?

2. Relevant equations

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Question concerning defining the general equation of a conic from 5-points

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