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Topic: Conic eccentricity through five points
Replies: 8   Last Post: Jul 22, 2013 2:08 PM

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Wally W.

Posts: 132
Registered: 6/15/11
Re: Conic eccentricity through five points
Posted: Jun 7, 2013 8:17 AM
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On Fri, 07 Jun 2013 07:14:10 -0400, Wally W. wrote:

>On Thu, 6 Jun 2013 06:20:30 -0700 (PDT), Narasimham wrote:
>

>>Find eccentricity of a conic in terms of 5 points (x1,y1) to (x5,y5).( as there are 5 constants in a x^2 + 2 h x y + b y^2 + 2 f x + 2 g y = 1 )
>>
>>TIA
>>Narasimham

>
>
>Five equations with five unknowns. The constants can be found.
>
>Then I would go here:
>
>https://en.wikipedia.org/wiki/Rotation_of_axes
>
>Starts with an equation similar to yours, with F = -1.
>
>Last section:
>Identifying rotated conic sections
>
>Convert the equation to the standard form of the known shape, and plug
>values into the equation for eccentricity.
>
>It seems that it would be very tedious with many opportunities for
>error, but doable.


Or more directly here:
<https://en.wikipedia.org/wiki/Conic_section#Eccentricity_in_terms_of_parameters_of_the_quadratic_form>




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