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笔者应用“几何画板”软件发现等轴双曲线的一个有趣性质,写出来与大家共享。如图1所示,A、B两点位于等轴双曲线x~2-y~2=λ(λ>0)不同的两支上,且关于原点O对称,C点是异于A、B两点的双曲线上任一点,过C点作其中一条渐近线的平行线交线段AB于D点,则CD平分∠ACB。下面加以证明。证明:若直线AC、BC中的一条斜率不存在,另一条为零,则显然成立。不妨设A(x_1,y_1)、B(-x_1,
I use the “geometric drawing board” software to find an interesting property of isometric hyperbola, write it out and share with you. As shown in Fig. 1, A and B are located on two different branches of the equiaxial hyperbola x ~ 2-y ~ 2 = λ (λ> 0), symmetrical about the origin O and point C is different from A and B At any point on the hyperbola of the two points, the point C of the parallel line intersecting the line AB on the point C as the point of the asymptotic line crosses the point C, and the CD is divided by ∠ ACB. Below to prove. Proof: If the line AC, BC in a slope does not exist, the other is zero, then obviously established. May wish to set A (x_1, y_1), B (-x_1,