The tangents drawn from a point \( P \) to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}....

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The tangents drawn from a point \( P \) to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) make angles \( \alpha \) and \( \beta \) with the major axis.
\( \mathrm{P} \)
Now, match the following lists:
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ List - I } & \multicolumn{2}{|c|}{ List - II } \\
\hline A. & If \( \alpha+\beta=\frac{c \pi}{2},(c \in \mathbb{N}) \), then the locus of \( P \) can be & P. & Circle \\
\hline B. & If \( \tan \alpha \cdot \tan \beta=c,(c \in \mathbb{R}) \) then the locus of \( P \) can be & Q. & Ellipse \\
\hline C. & If \( \tan \alpha+\tan \beta=c,( \) where \( c \in \mathbb{R}) \), then the locus of \( P \) can be & R. & Hyperbola \\
\hline D. & If \( \cot \alpha+\cot \beta=c,,( \) where \( c \in \mathbb{R}) \) then, the locus of \( P \) can be & S. & Pair of straight line \\
\hline
\end{tabular}
\begin{tabular}{lllll}
& A & B & C & D \\
(1) & R, S & P, Q, R, S & R, S & R, S \\
(2) & R & P, Q & P, R & Q \\
(3) & Q, R & S, P, R & Q, R & R, S
\end{tabular}
(4) none of these
.


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