I am trying to find the number of points of intersection of the affine plane curves $y=x^{2}$ and $y=x^{2}+1$.
I have homogenised to find $$YZ=X^{2}$$ $$YZ=X^{2}+Z^{2}$$ and deduced there is a point of intersection at $(0:1:0)$. Setting $Y=1$ I get the affine curves $z=x^{2}$ and $z=x^{2}+z^{2}$. According to Bezout there should be 4(?) points of intersection when considering over the field of complex numbers. Obviously $(0,0)$ is on both curves. I am however struggling to find the other 3.