In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

If the line joining the points $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta)$ is extended to the point $N(x, y)$ such that $AN: NB = b: a$,then

The line segment joining the points $(2, -3)$ and $(-5, 6)$ is divided by the $y$-axis in the ratio:

What is the distance between the points $(a, 0)$ and $(0, a)$?

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 polar coordinate of a point $P$ is $\left(2, -\frac{\pi}{4}\right)$. The polar coordinate of the point $Q$,which is such that the line joining $PQ$ is bisected perpendicularly by the initial line,is