is the Euclidean distance, in the complex plane, between

and

. Likewise,

is the Euclidean distance between

and

.

Now the locus of points

such that the sum of the distances between

and two given points is equal to a given constant (greater than the distance between the two points) is an ellipse.

You do the math to transform the equation to the form shown in your answer. Hint: use the Pythagorean theorem to determine the distances without using the absolute value symbol.

Good luck, and keep us posted.