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一、一道经典考题,一种被忽视运用的本质解法对如下例1的解答,解法一几乎不被师生们运用;而解法二、解法三是常见解法,为便于分析问题,笔者仍把解法二、三写出来.例1(1981年全国高考题)已知双曲线x~2-y~2/2=1,过点P(1,1)能否做一条直线l,与双曲线交于A,B两点,且点P是线段AB的中点?(人教A版选修2-1第62页B组第4题)解法一:(被忽视运用的本质解法)设A(x_1,y_1),B(x_2,y_2),根据点与坐标以及曲线与方程的对应关
First, a classic exam, a neglected use of the essence of the solution to the following example 1, the solution is almost not to be teachers and students to use; and solution two, solution three is common solution, in order to facilitate the analysis of the problem, the author still solution Two or three write out .Example 1 (1981 national college entrance examination) known hyperbolic x ~ 2-y ~ 2/2 = 1, too point P (1,1) can make a straight line l, and hyperbolic intersection (Point A is the midpoint of line segment AB?). Solution 1: The Intrinsic Solution of Neglected Application Let A (x_1 , y_1), B (x_2, y_2), according to the coordinates of the point and the corresponding relationship between the curve and the equation