
Re: Conic eccentricity through five points
Posted:
Jun 7, 2013 8:17 AM


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>

