Match the following lists: \begin{tabular}{|c|c|c|c|} \hline \multicolumn{2}{|r|}{ List-I } & \m....
0Match the following lists:
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{2}{|r|}{ List-I } & \multicolumn{2}{|c|}{ List-II } \\
\hline A. & \begin{tabular}{l}
The points common to the \\
hyperbola \( x^{2}-y^{2}=9 \) and the \\
circle \( x^{2}+y^{2}=41 \) are
\end{tabular} & P. & \( (-5,-4) \) \\
\hline B. & \begin{tabular}{l}
Tangents are drawn from the \\
point \( \left(0, \frac{-9}{4}\right) \) to the \\
hyperbola \( x^{2}-y^{2}=9 \). Then \\
the point of tangency may \\
have coordinates
\end{tabular} & Q. & \( (5,4) \) \\
\hline C. & \begin{tabular}{l}
The point which is \\
diametrically opposite to \\
point \( (5,4) \) with respect to \\
the hyperbola \( x^{2}-y^{2}=9 \) is
\end{tabular} & R. & \( (-5,4) \) \\
\hline \( \mathrm{D} \). & \begin{tabular}{l}
If \( \mathrm{P} \) and \( \mathrm{Q} \) lie on the \\
hyperbola \( x^{2}-y^{2}=9 \) such \\
that the area of the isosceles \\
triangle \( \mathrm{PQR} \), where \\
\( \mathrm{PR}=\mathrm{QR} \) is 10 sq. units and \\
\( \mathrm{R} \equiv(0,-6) \), then \( \mathrm{P} \) can have \\
the co-ordinates
\end{tabular} & \( \mathrm{S} \). & \( (5,-4) \) \\
\hline
\end{tabular}
\( \mathrm{P} \)
W
\begin{tabular}{lllll}
& A & B & C & D \\
(1) & P,Q,R,S & Q,R & P & P,S \\
(2) & Q,R & P,Q & R & P,S \\
(3) & P,S & Q,R & P & Q \\
(4) none of these & &
\end{tabular}
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