The equation of a line passing through the point $(1, 2)$ whose distance from the point $(3, 1)$ is the greatest is

The line passing through $\left(-1, \frac{\pi}{2}\right)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is:

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} = $

The length of the perpendicular from the origin to a line is $7$ and the line makes an angle of $150^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.

If $PS$ is the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$ and $R(7,3)$,then the equation of the line passing through $(1,-1)$ and parallel to $PS$ is

Find the equations of the lines parallel to the axes and passing through the point $(-2, 3)$.