If the points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $

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

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

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

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

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 $\frac{p}{q} + \frac{q}{p} =$