2. Let $B$ and $C$ be fixed points, neither of which lies on the plane $\alpha$, and let the moving point $A$ be on the plane $\alpha$, such that $\sin \angle A B C=\frac{1}{2}$. Then the locus of point $A$ is ( ).
(A) ellipse
(B) parabola
(C) hyperbola
(D) any of the above is possible
2. D.

The locus of point $A$ that satisfies $\sin \angle A B C=\frac{1}{2}$ is a conical surface with $B$ as the vertex and $B C$ as the axis (the angle between the generatrix and the axis is $30^{\circ}$). Now, point $A$ also needs to lie on plane $\alpha$, so its locus is the intersection of the conical surface and plane $\alpha$, which can be any of the three types of conic sections.