x=y/a,∴焦点F(0,1/4a),准线:y=-1/4aPQ斜率必然存在,设PQ:y=kx1/4a∴y=ax=kx1/4a∴ax-kx-1/4a=0由韦达定理x1x2=k/a,x1x2=-1/4a由抛物线第二定义:抛物线上的点到焦点的距离的距离等于到准线的距离∴p=|PF|=P到准线距离=y1-(-1/4a)=y11/4a,q=|FQ|=Q到准线的距离=y2-(-1/4a)=y21/4a∴1/p1/q=1/(y11/4a)1/(y21/4a)=1/(kx11/4a1/4a)1/(kx21/4a1/4a)=1/(kx11/2a)1/(kx21/2a)=[(kx21/2a)(kx11/2a)]/(kx11/2a)(kx21/2a)=[k(x1x2)1/a]/[kx1x2(k/2a)(x1x2)1/4a]=(k/a1/a)/[-k/4ak/2a1/4a]=[(k1)/a]/[(k1)/4a]=4a