Question

If $z=x+iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5i|=0$, then

• A. $x^2-y+3=0$
• B. $x+2y-4=0$
• C. $x^2+y-4=0$
• D. $x+2y+4=0$

Answer 1

The correct option is D $x+2y+4=0$

$|z-i|-|z+5i|=0$
So, $z$ lies on ${\perp }^r$ bisector of $(0,1)$ and $(0,-5)$
i.e., line $y=-2$
as $|z|=2$
$\Rightarrow z=-2i$
$x=0$ and $y=-2$
so, $x+2y+4=0$