《数学通报》2006年第10期刊登的第1631号问题是:过双曲线ax2-by2=1(a0,b0)的右焦点F作B1B2⊥x轴,交双曲线于两点B1、B2,B2F1交双曲线于B点,连结B1B交x轴于H点.求证:过H垂直于x轴的直线是双曲线的(左)准线(如图1).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 No. 1631, published in the 10th bulletin of Mathematics Bulletin, 2006, is that the right focal point F of the hyperbolic ax2-by2 = 1 (a0, b0) is taken as B1B2⊥x axis and the hyperbolic curve is at the two points B1, B2, B2F1 cross hyperbolic at point B, the intersection of B1B and cross the x-axis at point H. Prove: H perpendicular to the x-axis of the line is hyperbolic (left) alignment (Figure 1) Parameter equation, Menelaus theorem gives two kinds of evidence