If the portion of a line intercepted between the coordinate axes is divided by the point $(2, -1)$ in the ratio $3:2$,then the equation of that line is:

The equation of the line perpendicular to $x = c$ is

Two lines $L_1$ and $L_2$ passing through the point $P(1, 2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ units from $P$. Then the angles made by $L_1$ and $L_2$ with the positive $X$-axis are

If the three points $(3q, 0)$, $(0, 3p)$, and $(1, 1)$ are collinear, then which one is true?

Find the equation of the line passing through the point $(0, 2)$ making an angle of $\frac{2 \pi}{3}$ with the positive $x$-axis. Also,find the equation of the line parallel to it and crossing the $y$-axis at a distance of $2$ units below the origin.

The slope of the line passing through the origin,which makes an angle of $30^{\circ}$ with the positive direction of the $Y$-axis measured anticlockwise,is