I am needing to make a detailed comparison of the affine conics in $\mathbb{R}^2$ with that of the projective conics in $\mathbf{P}^2$
could only identify:
a) classification of non-degenerate conics
b) single pt given by $x^2 + y^2 = 0$
c) line $xy=0$
(e,f,g) empty set given by $x^2 + y^2 = -1$, $x^2 = -1$ or $0 = 1$
j) parallel lines $x(x-1)=0$
k) double line $x^2 = 0$
l) plane given by $0=0$
Can someone please help on this?