在中学代数中韦达定理占有很重要的位置,它将一元二次方程的根与其系数有机地联系起来。然而它在解析几何中的应用往往被有的学生忽视。在牵涉到直线与曲线相交的问题中,它所起到的作用非同小可,可以大大减少计算量。下面针对这个问题,用例题来说明。例1:圆系x~2+y~2-2(m-1)x+2(m+1)y+2m~2-2=0。求证平行于直线y=-x与圆系相交的直线,它在各圆上截取相等的弦。 In the middle school algebra, Vedic theorem occupies a very important position, which organically associates the root of a quadratic equation with its coefficient. However, its application in analytic geometry is often overlooked by some students. In the problems involving the intersection of a straight line and a curved line, it plays a very important role, which can greatly reduce the amount of calculations. Below for this problem, use examples to illustrate. Example 1: Circles x~2+y~2-2(m-1)x+2(m+1)y+2m~2-2=0. Verify that the line y=-x intersects the circle system parallel to the line. It cuts equal strings on each circle.