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If \({z}_{1},{z}_{2}\) are two distinct complex number such that \(\left|\frac{{z}_{1}-2{z}_{2}}{\frac{1}{2}-{z}_{1}{\ov…

Q1

If \({z}_{1},{z}_{2}\) are two distinct complex number such that \(\left|\frac{{z}_{1}-2{z}_{2}}{\frac{1}{2}-{z}_{1}{\overset{¯}{z}}_{2}}\right|=2\), then

[JEE Main 2024, 6 Apr (Shift 2)]

a

\(z_1\) lies on a circle of radius \(\frac{1}{2}\) and \(z_2\) lies on a circle of radius 1 .

b

both \(z_1\) and \(z_2\) lie on the same circle.

c

either \(z_1\) lies on a circle of radius 1 or \(z_2\) lies on a circle of radius \(\frac{1}{2}\)

d

either \(z_1\) lies on a circle of radius \(\frac{1}{2}\)or \(z_2\) lies on a circle of radius 1 .

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