4. $l 、 l^{\prime}$ are skew lines that are perpendicular to each other, $l$ is parallel to plane $\alpha$, and $l^{\prime}$ lies in plane $\alpha$. Then, the locus of points in plane $\alpha$ that are equidistant from $l 、 l^{\prime}$ is ( ).
(A) Line
(B) Ellipse
(C) Parabola
(D) Hyperbola
4. D.

As shown in Figure 3, in plane $\alpha$, take $l^{\prime}$ as the $x$-axis and the projection of $l$ in plane $\alpha$ as the $y$-axis to establish a Cartesian coordinate system. Then, the distance from a moving point $M(x, y)$ in plane $\alpha$ to $l^{\prime}$ is $|y|$, and the distance to $l$ is $\sqrt{x^{2}+a^{2}}$ (where $a$ is the distance between the skew lines $l$ and $l^{\prime}$).
Thus, $|y|=\sqrt{x^{2}+a^{2}}, y^{2}-x^{2}=a^{2}$.
Therefore, the required locus is a hyperbola.