The line x = 1, y = 2 is

The correct option is parallel to z-axis.

Let us understand why the line given by the equations $x=1$ and $y=2$ is parallel to the z-axis in three-dimensional space.

In three-dimensional Cartesian coordinate system $(x,y,z)$, any point on a line must satisfy the equations defining that line.
Here, the line is defined by the intersection of two planes:
1. The plane $x=1$, which is a plane parallel to the y-z plane.
2. The plane $y=2$, which is a plane parallel to the x-z plane.

For any point $(x,y,z)$ lying on this line, the x-coordinate must always be $1$ and the y-coordinate must always be $2$.
However, there is no restriction on the z-coordinate. This means the z-coordinate can take any real value, from $-\infty$ to $+\infty$.

Therefore, we can write the general coordinates of any point on this line as:
$(1,2,z)$

As the value of $z$ changes, the points move vertically upwards or downwards along a direction that is completely parallel to the z-axis (which is defined by the set of points $(0,0,z)$).
Since the x and y coordinates remain constant while only the z coordinate varies, the line runs parallel to the z-axis at a distance of $\sqrt{1^2+2^2}=\sqrt{5}$ units from it.