The equation of the line passing through the point $(-3, 1)$ and bisecting the angle between the coordinate axes in the second quadrant 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 $y$-intercept made by the line $x \cos \alpha + y \sin \alpha = a$ is:

Find the equation of the line which intersects the $y$-axis at a distance of $2$ units above the origin and makes an angle of $30^{\circ}$ with the positive direction of the $x$-axis.

The sum of the squares of the intercepts made by the line $5x - 2y = 10$ on the coordinate axes equals:

The equation of the straight line cutting off an intercept of $2$ from the negative direction of the $y$-axis and inclined at $30^\circ$ to the positive direction of the $x$-axis is: