Find the locus represented by $$\sqrt {(x-2)^2 + y^2} + \sqrt {(x+2)^2+y^2}=4$$
My Attempt:
Let $P(x,y)$ be any point on the locus. If we suppose $A(2,0)$ and $B(-2,0)$ any two points on the locus then from the above equation we have: $|PA| + |PB| = |AB|$
As you find out we have $$|PA| + |PB| = |AB|$$
so by triangle (in)equality we see that $P$ is on the segment $AB$. So $y=0$ and $|x|\leq 2$.