设中点坐标为(x,y),P(x1,y1),Q(x2,y2).依题意：x1^2+y1^2=16,x2^2+y2^2=16.两式相加有(x1+x2)^2+(y1+y2)^2-2(x1x2+y1y2)=32.又AP⊥AQ,故
(x1-2)(x2-2)+y1y2=0,整理得x1x2+y1y2-2(x1+x2)+4=0.又因为2x=x1+x2,2y=y1+y2.故代入上式有：4x^2+4y^2-2(4x-4)=32.整理得中点的轨迹方程为：(x-1)^2+y^2=7.不知对不对哈~自己再想想……小学妹加油哈~