Using the fact that |z1-z2| is the distance between two points z1 and z2, give a geometric argument that |z-4i|+|z+4i|=10 represents an ellipse whose foci are (0,4) and (0,-4). Can you help me get started, please?
With all due respect, you real problem is that you have no idea what an ellipse really is.
You might study this webpage.
For your ellipse the focii are $\displaystyle (0,4)~\&~(0,-4)$,. Thus the major axis is vertical.