在几何画板中,不能直接作出直线与圆锥曲线的两个交点以及过圆锥曲线上任一点的切线。本文试从解析几何中一道求点的轨迹的题目入手,探究用绘制辅助点法作直线与圆锥曲线的交点及过圆锥曲线上任一点的切线。这是一道大家熟知的解析几何题:已知点A是圆x2+y2=a2(a0)上任意一点, In the Sketchpad, you cannot directly make two intersections of a straight line and a conic curve, and a tangent to any point on a conic section. This article starts with the topic of solving the trajectory of a point in analytical geometry, and explores the point of intersection of a straight line with a conic curve and the tangent of any point on a conic section by the method of drawing auxiliary points. This is a well-known analytical geometry problem: the known point A is any point on the circle x2+y2=a2(a0).