How to represent point-at-infinity in affine coordinate In projective coordinates point-at-infinity can be identified with z=0. How to identify the point-at-infinity in affine coordinate.

Whether x=0 and y=0 can be considered as point-at-infinity in affine coordinate?
From a mathematical point of view this is not possible. I would say almost by definition because the point at infinity does not lie in the affine part. To be more precise:

Let $\mathbb P^2$ is the two dimensional projective space with coordinates $(x:y:z)$ and $\mathbb A^2 \subset \mathbb  P^2$ the affine part where $z \neq 0$ then one can see $X = x/z$ and $Y = y/z$ as coordinates on $\mathbb A^2$. Then $\mathbb P^2 \setminus \mathbb A^2$ is exactly the part where $z=0$ by definition. 

Now if $E$ is the curve given by $y^2z = x^3 + axz^2 +bz^3$, then there is exactly one point of $E$ in $\mathbb P^2 \setminus \mathbb A^2$. Indeed by setting $z=0$ one obtains $0 = x^3$ hence $x=0$ showing that (x:y:z) = (0:1:0) is the only point of $E$ not in $\mathbb A^2$. This point (0:1:0) is the point at infinity and does not lie in $\mathbb A^2$ hence you cannot represent (0:1:0) in affine coordinates.