(1)设P(x,y).则PA的斜率为y/(x-2),PB的斜率为y/(x+2).故
y^2/(x^2-4)=-3/4,
故P的轨迹C:x^2/4+y^2/3=1,是一个焦点在x轴上,长轴长4,短轴长2倍根号下3,焦距为2的椭圆.
(2)在EF垂直于y轴时,此直线为y=0,E(-2,0)F(2,0),M(0,0),k=0.
在EF不垂直于y轴时,设此直线为x=my+1/2,联立方程,有
(3m^2+4)y^2+3my-45/4=0,故M的纵坐标为-3m/(6m^2+8),
M(4/(6m^2+8),-3m/(6m^2+8)).k=m/(4m^2+4)=1/(4m+4/m),
由均值定理4m+4/m不小于8,故k的绝对值不大于1/8.
综上-1/8≤k≤1/8．