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Directrix of Ellipse

Let S1,S2 are...

Question

Let $S_{1}, S_{2}$ are foci of an ellipse, whose major axis length is $15$ units and $P$ be any point on the ellipse such that perimeter of triangle $P S_{1} S_{2}$ is $20$ units. If $e$ is the eccentricity of the ellipse, then $3 e =$

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Solution

Given, $2 a = 15$
and $P S_{1} + P S_{2} + S_{1} S_{2} = 20$
$\Rightarrow 2 a + 2 a e = 20$
$\Rightarrow 2 a (1 + e) = 20$
$\Rightarrow 15 (1 + e) = 20$
$\Rightarrow 3 e = 1$

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