The complex equation $|z-8-2i|+|z-5-6i| = 5$ looks like it is an equation of an ellipse but in reality it represents a line segment, why?
The equation of an ellipse is $|z-z_1|+|z-z_2|=2a$, where $z_1$ & $z_2$ are the focus points and $2a$ is the length of the major axis. The distance between $z_1$ & $z_2$ is $5$ which is equal to the major.
Please help me to understand under what conditions the equation $|z-z_1|+|z-z_2|=2a$ represents an ellipse.