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 $z=x+iy$
$|z-ai|=|z+ai|\Rightarrow |x+i(y-a)|=|x+i(y+a)|\Rightarrow \sqrt{x^2+(y-a{)}^2}=\sqrt{x^2+(y+a{)}^2}$
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.