A confirmation about $|z+1|+|z-1|=c, c=1,2, 3$; here $z$ is complex

Question

According to me $|z+1|+|z-1|=1$ represents no curve in $x-y$ (Argand plane). $|z+1|+|z-1|=2$ represents a line segment from $(-1,0)$ to $(1,0).$ Next, $|z+1|+|z-1|=3$ represents an ellipse. Could some one confirm/comment on my answers here.