1. Given sets
$$
\begin{array}{l}
A=\left\{(x, y) \mid y^{2}=8 x, x \in \mathbf{R}\right\}, \\
B=\left\{(x, y) \mid y=x^{2}, x \in \mathbf{R}\right\} .
\end{array}
$$

Then $A \cap B=(\quad)$.
(A) $[0,+\infty)$
(B) $\{(0,0),(2,4)\}$
(C) $\{0,2\}$
(D) $\{(0,0),(1,2 \sqrt{2})\}$
- 1. B.
$A \cap B$ represents the set of points formed by the intersection of the two parabolas. Solving the system of equations, we get
$$
(x, y)=(0,0),(2,4) \text {. }
$$