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58问答库 > 满足|z-z0|+|z+2i|=4的复数z在复平面上对应的点Z的轨迹是线段，则复数z0在复平面上对应的点的轨迹是_____

满足|z-z0|+|z+2i|=4的复数z在复平面上对应的点Z的轨迹是线段，则复数z0在复平面上对应的点的轨迹是_____

2025-04-07 12:13:05

推荐回答（1个）

回答（1）：

∵|z-z₀|+|z+2i|=4，且点Z的轨迹是线段，
∴z₀和-2i对应的点必然是Z的轨迹：线段上面2个端点，且线段的长为4，
∴Z点轨迹：线段，它是通过一个端点（0，-2）的任意线段，并且长度为4，
∴z₀点轨迹其实是圆心为（0，-2），半径为4的圆，
故答案为：以（0，-2）为圆心以 4 为半径的圆．

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