The equation of the smallest circle passing through the intersection of the line \( x+y=1 \) and...

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The equation of the smallest circle passing through the intersection of the line \( x+y=1 \) and the circle \( x^{2}+y^{2}=9 \) is
(a) \( x^{2}+y^{2}+x+y-8=0 \)
(b) \( x^{2}+y^{2}-x-y-8=0 \)
(c) \( x^{2}+y^{2}-x+y-8=0 \)
(d) none of these
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