For the conic, 5x2+4xy+5y2=9, find the direction of the principal axes, sketch the curve.
I found the eigenvalues as
3,7 but have no idea whether the 'new' equation is
is there a way to determine which 'way' it goes?
I took a guess and just continued using the first formula:
I found the eigenvectors by substituting the eigenvalues and got:
λ=3, V1 = (-1,1)
λ=7, V2 = (1,1)
I then thought the principal axes would therefore be:
1/√2 (-1,1) and 1/√2 (1,1)
yet the answer seems to indicate the principal axes as, (1,-1) and (1,1), why is that? I thought you had to normalise the vectors to find the principal axes..