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对于定比“λ”的应用,我们一般只停留在求点的坐标或以“λ”为参数求轨迹的问题中,而实际上,它还可以解决许多比较繁难的题目。下文将归纳二类问题,以供大家参考。一、证明线段相等例1 双曲线x~2/a~2-y~2/b~2=1的切点为p的切线交渐近线于A,B二点。求证:P点必平分线段AB。证明:因双曲线渐近线方程为y=±(b/a)x,可设A(x~1,(b/a)x_1)、B(X_2,-(b/a)x_2)为切线与渐近线的二交点。再设P点分线段AB的定比为λ,且P点的
For the application of ratio “λ”, we generally only stay in the coordinates of the point or the problem of trajectory with “λ” as the parameter. In fact, it can also solve many difficult problems. The following will summarize the second category for your reference. 1. Proof that the line segment is equal to the case 1. The tangent point of the hyperbola x~2/a~2-y~2/b~2=1 is p, and the tangent line is asymptote to A and B. Proof: P point must divide the line AB. Proof: Since the hyperbolic asymptote equation is y=±(b/a)x, we can set A(x~1,(b/a)x_1) and B(X_2,-(b/a)x_2) as tangents. The intersection with the asymptote. Set the ratio of the point AB of the P point again to λ, and the point P