Question

已知抛物线的顶点是坐标原点O,焦点F在X轴正半轴上,过F的直线l与抛物线交与A.B两点,且满足向量OA乘以向量OB等于-

Answer 1

设方程：y²=2px,A(x,y),B(x',y'),

∵xx'=p²/4,yy'=-p².

∴向量A×B=(x,y)(x',y')=xx' yy'=(p²/4)-p² =-3.

解得p=2.

∴抛物线方程：y²=4x.