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If \( \operatorname{Re}\left(\frac{z-1}{2 z+i}\right)=1 \), where \( z=x+i y \), then the point \( (x, y) \) lies on a […

Q1

If \( \operatorname{Re}\left(\frac{z-1}{2 z+i}\right)=1 \), where \( z=x+i y \), then the point \( (x, y) \) lies on a


[JEE Main 2020, 7 Jan (Shift 1)]

a

Straight line whose slope is \( \frac{3}{2} \)

b

Straight line whose slope is \( -\frac{2}{3} \)

c

Circle whose diameter is \( \frac{\sqrt{5}}{2} \)

d

Circle whose centre is at \( \left(-\frac{1}{2},-\frac{3}{2}\right) \)

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