8. What does the set of points belonging to lines that intersect one of two given skew lines and are parallel to the second one represent?
8. Let $a$ and $b$ be given skew lines. Through the point $A_{1} \in a$, draw a line $a_{1} \| b$. The intersecting lines $a$ and $a_{1}$ define a plane $\alpha$ to which they belong. On the line $a$, take another point $A_{2}$ and draw $a_{2} \| b$ through it. Since $b \| \alpha$, then $a_{2} \subset \alpha$ (if the line $a_{2}$ intersected the plane $\alpha$ at one point, then $\alpha$ would have to intersect the line $b$). Thus, all lines that intersect $a$ and are parallel to $b$ lie in the plane $\alpha$. It is easy to see that any point $M \in \alpha$ belongs to one of the considered lines, so the desired set coincides with the plane $\alpha$.