焦點F坐標(biāo)(0.5p,0),設(shè)直線L過F,則直線L方程為y=k(x-0.5p)
聯(lián)立y²=2px得k²x²-(pk²+2p)x+p²k²/4=0
由韋達定理得x1+x2=p+2p/k²
AB=x1+0.5p+x2+0.5p=x1+x2+p=2p+2p/k²=2p(1+1/k²)
因為k=tana,所以1+1/k²=1+1/tan²a
=(sin²a/sin²a)+(cos²a/sin²a)
=(sin²a+cos²a)/sin²a
=1/sin²a
所以AB＝2p（1+1/k²）=2p/sin²a
∵sin²a∈(0,1]
∴AB≥l2pl