问题补充:
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,
答案:
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=y1²/4
x2=y2²/4)
y1y2²/4-y1=y1²y2/4-y2
y1y2(y2-y1)=4(y1-y2)
y1y2=-4
x1x2=y1²y2²/16=1
OA*OB=x1x2+y1y2=1-4=-3