Exercise 3.1 in Hartshorne's Algebraic Geometry:
Show that any conic in $\mathbb{A}^2$ is isomorphic to $\mathbb{A}^1$ or $\mathbb{A}^1-\{0\}$.
when the conic given by $x^{2}+y^{2}-1$, what the coordinate ring of this one? Maybe $k[x]$? Cause I can project the circle to the affine line by deleted one point. But in topology they are not isomorphism. Then what the coordinate ring of circle?
Thanks advanced!