Question

If $z=x+iy$ and $|z-ai|=|z+ai|$ then the locus of $z$ is

• A. real axis
• B. imaginary axis
• C. $x=y$
• D. $x^2+y^2=1$

Answer 1

The correct option is A real axis

Let $z=x+iy$
$|z-ai|=|z+ai|$
$\Rightarrow |x+i(y-a)|=|x+i(y+a)|$
$\sqrt{x^2+(y-a{)}^2}=\sqrt{x^2+(y+a{)}^2}$
Squaring both the sides, we get,
$x^2+(y-a{)}^2=x^2+(y+a{)}^2$
$\Rightarrow y=0$, which is equation of real axis