《数学通报》2006年第9期数学问题(文[1])1631为:过双曲线x~2/a~2-y~2/b~2=1(a>0,b>0)的右焦点F作B_1B_2⊥x轴,交双曲线于两点B_1,B_2,B_2F_1交双曲线于B点,连结BB_1交x轴于H点.求证:过H垂直于x轴的直线l是双曲线的“左”准线.1几何证法探究文[2]中供题者分别运用双曲线的参数方程、梅涅劳斯定理给出了两种证明,具有较强的技巧 Mathematical Problem (Article [1]) 1631 is the result of the hyperbolic curve x ~ 2 / a ~ 2 ~ y ~ 2 / b ~ 2 = 1 (a> 0, b> 0) The right focus F for the B_1B_2⊥x axis, cross hyperbolic at two points B_1, B_2, B_2F_1 cross hyperbolic at point B, connecting BB_1 cross the x axis at point H. Prove that: H perpendicular to the x axis of the straight line l is hyperbola “Left ” guideline.1 geometric evidence method to explore the text [2] for the author respectively hyperbolic parametric equation, Menelaus theorem gives two kinds of proof, with strong skills