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 $y$-intercept of the line passing through $A(6, 1)$ and perpendicular to the line $x - 2y = 4$ is:

Find the equation of the line,which cuts off intercepts on the axes whose sum and product are $1$ and $-6,$ respectively.

Suppose a line makes an angle of $120^{\circ}$ with the positive direction of $X$-axis. If the length of the perpendicular from the origin to that line is $4$,then the equation of the line is

The equation of a line with slope $-\frac{1}{\sqrt{2}}$ and making an intercept of $2 \sqrt{2}$ units on the negative direction of the $y$-axis is:

$A$ straight line through the point $P(1, 2)$ makes an angle $\theta$ with the positive $X$-axis in the anticlockwise direction and meets the line $x + \sqrt{3}y - 2\sqrt{3} = 0$ at $Q$. If $PQ = \frac{1}{2}$,then $\theta =$