1) Check the sign of the discriminant:
2) Let be the respective coefficients after the rotation. Calculate to get So .
I'm not sure this is where I should put this, but I didn't see anywhere else:
1)
Using the determinant of a matrix representing a conic,
[a b d]
[b c e]
[d e f]
where the equation of the conic is
ax^2=2bxy+cy^2+2dx+2ey+f=0
and the determinant of the top left 2-by-2 matrix, how would you classify the conic?
2) (Refering to the d and e of the previous question)
Show that d^2+e^2 stays the same under a rotation of axes, in other words, the matrix is multiplied by
[cos(z) -sin(z) 0]
[sin(z) cos(z) 0]
[0 0 1]
Note: It's a 3x3 matrix
Thanks in advance!