question_answer

If P is the affix of \[z\] in the Argand diagram and P moves so that \[\frac{z-i}{z-1}\] is always purely imaginary, then the locus of z is \[(Note\text{ }:\text{ }i\text{ =}\sqrt{-1})\]

A)  circle with centre \[\left( \frac{1}{2},\frac{1}{2} \right)\] and radius \[\frac{1}{\sqrt{2}}\]

B)  circle with centre \[\left( \frac{-1}{2},\frac{-1}{2} \right)\] and radius \[\frac{1}{\sqrt{2}}\]

C)  circle with centre (2, 2) and radius \[\frac{1}{2}\]

D)  circle with centre \[\left( \frac{-1}{2},\frac{-1}{2} \right)\] radius \[\frac{1}{2}\]