在“圆锥曲线”一章的学习中,我们经常遇到直线与椭圆相交求弦长、求轨迹方程的问题,通常的做法是将直线方程与椭圆方程联立,消元、转化为一元二次方程,再运用韦达定理来求解,但这一转化往往伴随着比较复杂的运算.其实,这类问题也可以从直线与椭圆的交点出发,先设出交点的坐标,再利用曲线上的点与方程的关系来转化,常常能起到化繁为简的效果. In the study of the “conical curve” chapter, we often encounter the problem of finding the length of the chord and the trajectory equation by intersecting the straight line and the ellipse. The common practice is to combine the linear equation with the elliptic equation and eliminate the yuan and convert it into a quadratic element. The equations are then solved using Weddah’s theorem, but this transformation is often accompanied by more complex operations. In fact, this type of problem can also be based on the intersection of a straight line and an ellipse, setting the coordinates of the point of intersection first, and then using points on the curve. Transformation with the relationship between equations can often be used to simplify the effect.