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Suppose the circle having equation \( x^{2}+y^{2}=3 \) intersects the rectangular hyperbola \( x y=1 \) at points \( A, B, C \), and \( D \). The
\( \mathrm{P} \) equation \( x^{2}+y^{2}-3+\lambda(x y-1)=0, \lambda \in R \), represents

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(1) a pair of lines through the origin for \( \lambda=-3 \)
(2) an ellipse through \( A, B, C \), and \( D \) for \( \lambda=-3 \)
(3) a parabola through \( A, B, C \), and \( D \) for \( \lambda=-3 \)
(4) a circle for any \( \lambda \in R \)
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