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 K−15 is equal to

A and B are on opposite sides of y - axis. Reflection of A (-3, 2) is y - axis is A'=(3,2) so that A',B will be on the same side of PEquation of A'B is   y−2=−3(x−3)⇒y−2=−3x+93x+y=11This meets y - axis at Q (0, 11)Q is requried position of P so that k = 11∴k−15=105=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.