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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.
The locus of the mid-point of \( A B \) is
(a) \( \left(x-\frac{a}{2}\right)^{2}+y^{2}=\frac{b^{2}}{4} \)
(b) \( \left(x-\frac{a}{2}\right)^{2}+y^{2}=\frac{a^{2}}{4} \)
(c) \( \left(x-\frac{b}{2}\right)^{2}+y^{2}=\frac{a^{2}}{4} \)
(d) \( \left(x-\frac{b}{2}\right)^{2}+y^{2}=\frac{b^{2}}{4} \)
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