- If $\displaystyle z=x+iy$ satisfies $\displaystyle \mid z-4 \mid + \mid z+4 \mid =10$ show that

$\displaystyle (x/5)^2+(y/3)^2=1$

- Conversely, if x and y satisfy $\displaystyle (x/5)^2+(y/3)^2=1$, then show that $\displaystyle z=x+iy$ satisfies $\displaystyle \mid z-4 \mid + \mid z+4 \mid =10$.

Not a clue how to do this, nothing seems to work.