Assumptions

- A
**non-degenerate conic curve**(**NDCC**), C , is**the intersection of****a plane**, $\pi$,**with****a cone**that**does not pass through**the vertex of the cone, $O$.

- We can assign
**3 dimensional Cartesian coordinates**so that $O = (0,0,0)$ and $\pi =\{(x,y,z): z=1\}$.

- C
is a NDCC
**if and only if****real irreducible polynomial**$P(x,y)=Ax^2 + Bxy + Cy^2 + Dx + Ey + F$ with

$A, B$, and $C$**not all 0****AND**C $ = \{(x,y,1): P(x,y) = 0\}.$