Let complex numbers \( \alpha \) and \( \frac{1}{\bar{\alpha}} \) l...
Let complex numbers \( \alpha \) and \( \frac{1}{\bar{\alpha}} \) lie on circles
P \( \left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}=r^{2} \) and
W \( \left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}=4 r^{2} \), respectively. If \( z_{0}=x_{0}+i y_{0} \) satisfies the equation \( 2\left|z_{0}\right|^{2}=r^{2}+2 \), then \( |\alpha| \) equals to
[JEE Advanced 2013, 2M]
(a) \( \frac{1}{\sqrt{2}} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{1}{\sqrt{7}} \)
(d) \( \frac{1}{3} \)
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