The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

The length of the perpendicular from the origin to a line is $9$ and the perpendicular makes an angle of $120^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.

The system of linear equations $ax - y + 2 = 0$ and $x + ay + 3 = 0$ has a unique solution. Then,the set of values of $a$ is . . . . . . .

The equation of the line passing through the origin and the point $(a \cos \theta, a \sin \theta)$ is .....

If two vertical poles of heights $20\,m$ and $80\,m$ stand apart on a horizontal plane,then the height (in $m$) of the point of intersection of the lines joining the top of each pole to the foot of the other is:

The equation of the straight line making equal intercepts on the axes and passing through the point $(2, 4)$ is