List of top Mathematics Questions asked in AP EAPCET

If $z = x + iy , x , y \in R$ and the imaginary part of $\frac{\bar{z} - 1}{\bar{z} - i}$ is $1$ then the locus of $z$ is

Which of the following is divisible by $x^{2}-y^{2}, \forall x\ne y$?