Determine set of points in the complex plane that satisfies the following equation

Question

Thanks for taking your time.

I've been given the following problem:

Determine and plot set of points in the complex plane that satisfies the following equation

$ |z-2| + |z+2|=5 $

where $ z = x+iy$.

My first approach was to square both sides, but what I ultimately get is the square of a binomial, which when expanded gives me the product of square roots:

$ 2\sqrt{((x+2)^2+y^2)((x-2)^2+y^2)}$

which I don't know what to do with.

Can anyone provide some insight? Tanks!

Answer 1

Hint:

• Do you know what is a geometric meaning of $|z-w|$?
• Do you know the definition of particular conic sections?