(A) A hyperbola, having the transverse axis of length \( 2 \sin \theta \), is confocal with the ellipse \( 3 x^{2}+4 y^{2}=12 \). Then its equation is:
[IIT-JEE 2007]
(a) \( x^{2} \operatorname{cosec}^{2} \theta-y^{2} \sec ^{2} \theta=1 \)
(b) \( x^{2} \sec ^{2} \theta-y^{2} \operatorname{cosec}^{2} \theta=1 \)
(c) \( x^{2} \sin ^{2} \theta-y^{2} \cos ^{2} \theta=1 \)
(d) \( x^{2} \cos ^{2} \theta-y^{2} \sin ^{2} \theta=1 \)
(B) Match the statements in Column-I with the properties in Column-II. [IIT-JEE 2007]
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|}{ Column-I } & \multicolumn{1}{|c|}{ Column-II } \\
\hline (a) & Two intersecting circles & (p) & have a common tangent \\
(b) & Two mutually external circles & (q) & have a common normal \\
(c) & Two circles, one strictly inside the other & (r) & do not have a common tangent \\
(d) & Two branches of a hyperbola & (s) & do not have a common normal \\
\hline
\end{tabular}
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