(1)设P点坐标为(x,y),则B点坐坐为(2x-1,2y).依题意有｜BF｜/｜2x-1-(-1) ｜｜=｜(2x-1)-1｜/｜BF｜=e,即 (2x-2)2+4y2=2x(2x-2),∴y2=x-1(x＞1),故P点的轨迹是以(1,0)为顶点,x国轴为对称轴,开口向右的抛物线(不合顶点).
(2)｜PM｜=√[(x-m)^2+y^2] =√[x^2-(2m-1)x+m^2-1] =√{[x-(2m-1)/2]^2+m-5/4} (x＞1),当(2m-1)/2＞1,即m＞3/2时,｜PM｜min=√[(4m-5)/2],当 (2m-1)/2≤1,即m≤3/2时,｜PM｜无最小值.