抛物线标准方程:x^2=y/a
F(0,1/(4a)),设P(x1,y1) Q(x2,y2),
PQ平行于X轴时,方程为:y=1/(4a),p=q=1/(2a),1/p+1/q=4a
PQ不平行于X轴时,设其方程为x=k(y-1/(4a))
代入抛物线方程得:y=ak^2*(y-1/(4a))^2
16ay=k^2(4ay-1)^2
16(aky)^2-(8ak^2+16a)y+k^2=0
y1+y2=1/(2a) + 1/(ak^2)
y1y2=1/(16a^2)
准线:y=-1/(4a)
PF=y1+1/(4a),FQ=y2+1/(4a)
p+q=y1+y2+1/(2a)=(k^2+1)/(ak^2)
pq=y1y2+(y1+y2)/(4a)+1/(4a)^2
=1/(16a^2) + 1/(8a^2) + 1/(4a^2k^2) + 1/(16a^2)
=(k^2+1)/(4a^2k^2)
1/q+1/p=(p+q)/(pq)=4a
综上可知,等于4a.
C