Talk:Matrix representation of conic sections

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You have new messages (last change).

My question is this,

"what do the eigenlines of a conic's assosiated matrix correspond to, and why?"

The ellipse 17x^2 + 12xy +8y^2 = 1

may be assosiated with (x,y) (17 6) (x)

                             (6 8) (y)

having eigenvectors a(1,-2) and b (2,1).

My understanding of eigenvectors are that they are vectors that are not changed when transformed by the matrix.

I'm guessing there's a relationship between the focus and directrix of a conic and its eigenlines. But I can't seem to find out what that relationship is anywhere.

I'm not good enough at sums to figure it out for myself, so if you can explain this I'd be most pleased.

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