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圆锥曲线的中点弦问题是解析几何中的一类常见问题.对于求解以定点为中点的弦所在直线方程的问题,许多同学习惯于利用“点差法”先求直线斜率:即首先设弦的两端点坐标为A(x_1,y_1),B(x_2,y_2),代入圆锥曲线方程,将得到的两个方程相减,从而得到弦中点坐标与所在直线的斜率的关系,使问题得以解决.此方法巧妙地将斜率公式和中点坐标公式结合起来,设而不求,代点作差,可以减少计算量,提高解题
The midpoint chord problem of conic curves is a common problem in analytical geometry. For the problem of solving the linear equation where the fixed point is the midpoint of the string, many students are accustomed to using the “difference method” to seek the slope of the line first: The coordinates of the two ends of the string are A(x_1,y_1), B(x_2,y_2), and they are substituted into the conic section equation. The two equations are subtracted to obtain the relationship between the midpoint of the string and the slope of the straight line. The problem can be solved. This method skillfully combines the slope formula with the midpoint coordinate formula. The design is not required, and the difference between points is used to reduce the amount of calculation and increase the problem solving.