A(x1,y1) 、B(x2,y2)
∵AB中点纵坐标为1/2,
∴ y1+y2=1
∵y1y2=-p²,
∴y1^2+y2^2-2p^2=1
∴2px1+2px2-2p^2=1
2p(x1+x2-p)=1
分别过A,B向准线x=-p/2引垂线
垂足依次为A1,B1,则
AF=AA1=x1+p/2,BF=BB1=x2+p/2
∴AB=AF+BF=x1+x2+p=3
∴ x1+x2=3-p
∴2p(3-2p)=1
∴4p^2-6p+1=0
∴p=(3±√5)/4