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If $p$ is any point on the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$, and $S$ and $S^{\prime}$ are the foci, then $P S+P S^{\prime}=$
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Verified Answer
The correct answer is:
12
We have, equation of ellipse is
$$
\begin{aligned}
&\quad \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 \Rightarrow \frac{x^{2}}{(6)^{2}}+\frac{y^{2}}{(4)^{2}}=1 \\
&\therefore \quad a=6, b=4
\end{aligned}
$$
Now, $P S+P S=2 a=2 \times 6=12$
$$
\begin{aligned}
&\quad \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 \Rightarrow \frac{x^{2}}{(6)^{2}}+\frac{y^{2}}{(4)^{2}}=1 \\
&\therefore \quad a=6, b=4
\end{aligned}
$$
Now, $P S+P S=2 a=2 \times 6=12$
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