Find the distance of the point $P(-8, 6)$ from the origin.

The line joining $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta),$ where $a \neq b,$ is produced to the point $M(x, y)$ such that $AM : MB = b : a$. Then,$x \cos \frac{\alpha+\beta}{2} + y \sin \frac{\alpha+\beta}{2}$ is equal to

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

The coordinates of the point dividing internally the line segment joining the points $(4, -2)$ and $(8, 6)$ in the ratio $7 : 5$ are:

If the portion of a straight line intercepted between the coordinate axes is divided by the point $(2,3)$ in the ratio $2:3$,then the product of the intercepts made by this line on the axes is