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以空间图形为背景的平面上的点的轨迹问题近年已在高考卷上频频出现.这类题以空间直线与平面的位置关系为依托,研究平面解析几何的点的轨迹.解答这类题的关键是要能化空间问题为平面问题.具体可从以下两个方面考虑(客观题也可采用其他特殊方法解决).一、化空间问题为平面问题,利用曲线的定义推证轨迹例1(2004年北京)如图1,在正方体ABCD-A1B1C1D1中,P是侧面BB1C1C内一动点,若P到直线BC与直线C1D1的距离相等,则动点P的轨迹所在的曲线是()
The problem of trajectory of a point on a plane with a spatial pattern as a background has frequently appeared on the college entrance examination paper in recent years. This type of problem relies on the positional relationship between space lines and planes to study the trajectory of plane analytical geometry points. The key is to be able to solve the spatial problem as a planar problem. It can be considered from the following two aspects (the objective problem can also be solved by other special methods). 1. The space problem is a planar problem, and the trajectory is derived from the definition of the curve. Beijing, 2004) As shown in Figure 1, in the box ABCD-A1B1C1D1, P is a moving point in the side BB1C1C. If the distance from P to the straight line BC is equal to the straight line C1D1, the curve where the moving point P is located is ()