设A(x1,y1).B(x2,y2),
y²=2x.焦点(1/2,0).过其焦点的直线y=k(x-1/2)
代入得,k²x²-(k²+2)x+k²/4=0.
x1+x2=1+2/k².x1x2=1/4.
y1y2=k²(x1-1/2)(x2-1/2)=k²[x1x2-(x1+x2)/2+1/4]
=k²[1/2-1/2-1/k²]=-1.
向量OA乘向量OB=x1x2+y1y2=1/4-1=-3/4.
设A(x1,y1).B(x2,y2),
y²=2x.焦点(1/2,0).过其焦点的直线y=k(x-1/2)
代入得,k²x²-(k²+2)x+k²/4=0.
x1+x2=1+2/k².x1x2=1/4.
y1y2=k²(x1-1/2)(x2-1/2)=k²[x1x2-(x1+x2)/2+1/4]
=k²[1/2-1/2-1/k²]=-1.
向量OA乘向量OB=x1x2+y1y2=1/4-1=-3/4.