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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 $P S+P S^{\prime}$ is equal to
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12
Given ellipse is $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$
Here, $\quad a^{2}=36, b^{2}=16$
Since, $a>b$, so the sum of the focal distance of any point $P$ on the ellipse is $P S=P S^{\prime}+2 a$
$\Rightarrow \quad P S+P S^{\prime}=2 \times 6$
$\Rightarrow \quad P S+P S^{\prime}=12$
Here, $\quad a^{2}=36, b^{2}=16$
Since, $a>b$, so the sum of the focal distance of any point $P$ on the ellipse is $P S=P S^{\prime}+2 a$
$\Rightarrow \quad P S+P S^{\prime}=2 \times 6$
$\Rightarrow \quad P S+P S^{\prime}=12$
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