12.4. 7 * As shown in the figure, in the cube $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, there is a point $M$ on the side face $A A^{\prime} B^{\prime} B$ that is equidistant from the two lines $A B$ and $B^{\prime} C^{\prime}$. Then, the trajectory of $M$ is ( ).
(A) a part of a parabola
(B) a part of a hyperbola
(C) a part of an ellipse
(D) a line segment
And, the distance from $M$ to point $B^{\prime}$ is equal to the distance from $M$ to line $A B$. Therefore, the locus of $M$ is part of a parabola. Hence, the answer is A.