Choice A is the correct answer.

1. Set equal: $x^2 + 1 = 2x$.
2. Rearrange: $x^2 - 2x + 1 = 0$.
3. Factor: $(x - 1)^2 = 0$.
4. Solve: $x = 1$ (one repeated solution, meaning the line is tangent).
5. Find y: $y = 2(1) = 2$.
6. Point: $(1, 2)$.

Choice B is incorrect because $y eq 1$. Choice C is incorrect because $x eq 2$. Choice D is incorrect.