Analysis: Make diameter AC, connect CP to get △APC∽△PBA, and use AP/AC=BP/AP to get Y = (1/8) x 2, so x-y = X-[( 1/8) x 2] =

Answer:

Solution: As shown in the figure, make diameter AC and connect CP.

∴∠CPA=90，

∫AB is tangent,

∴CA⊥AB，

∵PB⊥l，

∴AC∥PB，

∴∠CAP=∠APB，

∴△APC∽△PBA，

∴AP/AC=BP/AP，

PA = x, PB=y, radius 4,

∴x/8=y/x，

∴y=( 1/8)x^2，

∴x-y=x-[( 1/8)x^2]=-[( 1/8)x^2]+x=-[ 1/8](x-4)^2+2，

When x=4, the maximum value of x-y is 2,

So the answer is: 2.