8.设O为坐标原点,A、B为抛物线y2=4x上两点,F为抛物线的焦点,向量AF=λ向量FB（∈R),则向量OA·向量OB=A.3λ B.3 C.-3λ D.-3请求详解,
问题描述：
8.设O为坐标原点,A、B为抛物线y2=4x上两点,F为抛物线的焦点,向量AF=λ向量FB（∈R),则向量OA·向量OB=
A.3λ B.3 C.-3λ D.-3
请求详解,
答
选D焦点F(1,0)设A(x1,y1) B(x2,y2)y1/(x1-1)=y2/(x2-1)y1x2-y1=x1y2-y2( x1=y1²/4x2=y2²/4)y1y2²/4-y1=y1²y2/4-y2y1y2(y2-y1)=4(y1-y2)y1y2=-4x1x2=y1²y2²/16=1OA*OB=x1x2+y1y2=1-4=-...