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六年制重点中学高中数学课本《解析几何》P.111的第8题:“过抛物线y~2=2px的焦点的一条直线和这抛物线相交,两个交点的纵坐标为y_1,y_2求证:y_1y_2=-p~2”。若设两个交点的横坐标为x_1,x_2,由y_1y_2=-p~2,易知x_1x_2=p~2/4,这就是说“抛物线焦点弦(经过焦点,并且两个端点在抛物线上的线段)的两个端点的横坐标之积是常数,纵坐标之积也是常数”。此结论很重要,它反映了抛物线焦点弦的一个重要性质。解题时,为了减少引进参数,若设抛物线y~2=
In the sixth year of the six-year key middle school mathematics textbook “Analytic Geometry” P.111, “a line that passes the focus of the parabola y~2=2px intersects with this parabola. The y-coordinates of the two intersections are y_1 and y_2. Y_1y_2=-p~2”. If we set the abscissa of the two intersections as x_1,x_2 from y_1y_2=-p~2, we can easily know x_1x_2=p~2/4, which means that the parabola focus chord (passes the focus and the two endpoints are on the parabola The product of the abscissas of the two endpoints of a line segment is a constant, and the product of the ordinate is also a constant." This conclusion is very important, it reflects an important property of the parabolic focal string. To solve the problem, in order to reduce the introduction of parameters, if you set the parabola y~2=