直線y=-2x-1過2,3,4象限,焦點在x軸與直線相交
∴拋物線在2,3象限 ∴焦點(-p/2,0) ,
拋物線過原點,設(shè)方程 ：y^2=-2px (p>0)
將直線代入拋物線方程：(-2x-1)^2=4x^2+4x+1=-2px 4x^2+(4+2p)x+1=0
x1+x2=-(4+2p)/4 ,x1x2=1/4
|AB|^2=(x1-x2)^2+(y1-y2)^2=(5√3)^2
=(x1-x2)^2+4(x1-x2)^2
=5(x1-x2)^2
=5[(x1+x2)^2-4x1x2]
=5[(-(4+2p)/4)^2-4*1/4]
=5[(p+2)^2-1]
=25*3
=> (p+2)^2-1=15 解得p=2 (p=-6舍棄)
∴拋物線方程為：y^2=-2px=-4x