设A(x1,y1),B(x2,y2)
将y=2x+1代入y^2=2px得4x^2+(4-2p)x+1=0
x1+x2=(p-2)/2,x1*x2=1/4
弦长公式：|AB|^2=(1+k^2)* |x1-x2|=5[(x1+x2)^2-4x1*x2]=15
解得p=6或p=-2
∴抛物线方程为y^2=12x或y^2=-4x