Consider the two circles \( C_{1}: x^{2}+y^{2}=a^{2} \) and \( C_{2}: x^{2}+y^{2}=b^{2}(ab) \). ...

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Consider the two circles \( C_{1}: x^{2}+y^{2}=a^{2} \) and \( C_{2}: x^{2}+y^{2}=b^{2}(ab) \). Let \( A \) be a fixed point on the circle
\( \mathrm{P} \)
\( C_{1} \), say \( A(a, 0) \) and \( B \) be a variable point on the circle \( C_{2} \). The
W line \( B A \) meets the circle \( C_{2} \) again at \( C \). 'O' being the origin.
If \( (O A)^{2}+(O B)^{2}+(B C)^{2}=\lambda \), then \( \lambda \in \)
(a) \( \left[5 b^{2}-3 a^{2}, 5 b^{2}+a^{2}\right] \)
(b) \( \left[4 b^{2}, 4 b^{2}+a^{2}\right] \)
(c) \( \left[4 a^{2}, 4 b^{2}\right] \)
(d) \( \left[5 b^{2}-3 a^{2}, 5 b^{2}+3 a^{2}\right] \)
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