- #1

wawar05

- 4

- 0

A conic is a subset of P2 given by a homogenous quadratic equation:

aX^2 + bY^2 + cZ^2 + dXY + eXZ + fYZ = 0

why is it homogeneous?

meanwhile, it suitable coordinates we have aX^2 + bY^2 + cZ^2 = 0, with a, b, c element {0, 1, -1}.

why the part of dXY + eXZ + fYZ can be erased?

what is the difference of degenerate conic and non-degenerate conic?