Explanation

(c)
Let $P,\ A,\ B$ represent complex numbers $z,\ 1 + 0i,\ - 1 + 0i$ respectively, then
$|z - 1| + |z + 1| \leq 4\ \ \Rightarrow \ \ \ \ \ PA + PB \leq 4$
$\Rightarrow \ \ \ P$ moves in such a way that the sum of its distance from two fixed points is always less than or equal to 4
$\Rightarrow$ Locus of $P$ is the interior and boundary of ellipse having foci at (1, 0) and (-1, 0)