1. The problem statement, all variables and given/known data 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 3(x')2+7(y')2 or 7(x')2+3(y')2 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..