Question

The number of possible integral value(s) of $k$ for which the equation
$|z+i|-|z-i|=k,k>0$ represents a hyperbola is

Answer 1

$|z-z_1|-|z-z_2|=k$ represent hyperbola if $k<|z_1-z_2|$
So, $|z+i|-|z-i|=k$ represents hyperbola if $k<|i-(-i)|$
$\Rightarrow k<2$
$\therefore 0<k<2(\because k>0)$
Clearly, only $1$ integral value is possible.