The points which trisect the line segment joining the points $(0, 0)$ and $(9, 12)$ are

Find the distance between the points $P \left( 3, -\frac{\pi}{6} \right)$ and $Q \left( 4, \frac{\pi}{3} \right)$ in polar coordinates.

If the line $2x - y - 4 = 0$ divides the line segment joining the points $(2, -1)$ and $(1, -4)$ at the point $(a, b)$ in the ratio $m:n$,then $4(a - b(\frac{m}{n})^2) = $

The point $A$ divides the join of the points $(-5, 1)$ and $(3, 5)$ in the ratio $k : 1$. The coordinates of the points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively. If the area of the triangle $ABC$ is $2$ square units,then $k =$

Find a point on the $x$-axis,which is equidistant from the points $(7, 6)$ and $(3, 4)$.

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to