If the line $2x - 3y + 4 = 0$ divides the line segment joining the points $A(-2, 3)$ and $B(3, -2)$ in the ratio $m:n$,then the point which divides $AB$ in the ratio $-4m:3n$ is

Find the coordinates of the point that divides the line segment joining the points $(3, -1)$ and $(3, 4)$ externally in the ratio $2 : 3$.

If the line $2x + y = k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ internally in the ratio $3:2$,then $(k+1):(k-1) =$

The distance of the midpoint of the line segment joining the points $(a \sin \theta, 0)$ and $(0, a \cos \theta)$ from the origin is:

The points of trisection of the line segment joining the points $(3, -2)$ and $(-3, -4)$ are

The line $2x + y - 3 = 0$ divides the line segment joining the points $A(1, 2)$ and $B(-2, 1)$ in the ratio $a : b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3a}, -3\right)$ and $Q\left(-3, -\frac{b}{3a}\right)$ in the ratio $p : q$,then $\frac{p}{q} + \frac{q}{p} =$