Given $P-R-Q$ and if $\frac{PR}{PQ} = \frac{2}{7}$,then $R$ divides $\overline{PQ}$ from $Q$ in the internal division ratio $\ldots \ldots \ldots \ldots$

$A(k, 2)$ and $B(3, 5)$ are the given points. If the point $P(t, t)$ divides the line segment $\overline{AB}$ in the ratio $k:1$ starting from $A$, find the value of $k$.

$A (1, -2)$ and $B (-7, 1)$ are the given points. Find $P$ on the line segment $AB$ such that $P$ lies on the extension of $AB$ (as indicated by $P-A-B$ order,though the condition $3AP = 5AB$ implies $P$ is outside the segment $AB$) and $3AP = 5AB$.

Find the value of $k$ if the points $A(2, 3)$,$B(4, k)$,and $C(6, -3)$ are collinear.

In which ratio does the $Y-$axis divide the line segment joining $A (-4, 1)$ and $B (1, 1)$ from $A$ (in $:1$)?

In what ratio does the point $(-4, 6)$ divide the line segment joining the points $A(-6, 10)$ and $B(3, -8)$?