$A(-3,2),B(2,5)$ be two points. If the point P (O, K) on y - axis, such that $|PA-PB|$ is greatest, then $\frac{K-1}{5}$ is equal to

A and B are on opposite sides of y - axis. Reflection of A (-3, 2) is y - axis is $A\text{'}=(3,2)$ so that $A\text{'},B$ will be on the same side of P
Equation of $A\text{'}B$ is   $y-2=-3(x-3)$$\Rightarrow y-2=-3x+9$

$3x+y=11$
This meets y - axis at Q (0, 11)
Q is requried position of P so that k = 11

$\therefore \frac{k-1}{5}=\frac{10}{5}=2$

(Since difference of two sides of a triangle is smaller than the thrid side)
Note: We know that $|PA-PB|$ will be greatest is P lies on the line containing A and B, rather A and B must lie on the same side of P.