Find the equation of the line passing through the point $(1, 2)$ and perpendicular to the line $y = 3x - 1$.

The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

Find the angle between the $x$-axis and the line joining the points $(3, -1)$ and $(4, -2).$ (in $^{\circ}$)

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units,which makes an angle of $135^{\circ}$ with the $X$-axis,then the equation of the line is

Find the equation of the line perpendicular to the line $x-7y+5=0$ and having $x$-intercept $3$.

If a line $L$ passing through the point $A(-2, 4)$ makes an angle of $60^{\circ}$ with the positive direction of $X$-axis in the anti-clockwise direction and $B(p, q)$ lying in the $3^{\text{rd}}$ quadrant is a point on $L$ at a distance of $6$ units from the point $A$,then $\sqrt{p^2+q^2-8q} = $