Question

If $Z=x+iy$ and ${}^{\prime }{a}^{\prime }$ is a real number such that $|z-ai|=|z+ai|$, then locus of $z$ is

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

Answer 1

The correct option is A x-axis

We have $|z-ai|=|z+ai|$

$\Rightarrow {|z-ai|}^2={|z+ai|}^2$

$\Rightarrow {|x+i(y-a)|}^2={|x+i(y+a)|}^2$

$\Rightarrow x^2+{(y-a)}^2=x^2+{(y+a)}^2$

$\Rightarrow 4ay=0$

$\Rightarrow y=0$ which is $x-axis$