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ISI2015-DCG-42

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In an ellipse, the distance between its foci is $6$ and its minor axis is $8$. hen its eccentricity is

  1. $\frac{4}{5}$
  2. $\frac{1}{\sqrt{52}}$
  3. $\frac{3}{5}$
  4. $\frac{1}{2}$
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The distance between two focii of ellipse is $2ae$ . Also , $c^{2}=\sqrt{a^{2}-b^{2}}$  where $c$ denotes the  distance between the focus and the origin.

Given, $2b=8$  $\Rightarrow$   $b=4$

$\therefore$  $2ae=6$  or $ae=3$  $c=3$

So, $3=\sqrt{a^{2}-16}$   $\Rightarrow$   $a=5$

So, $ae=3$   $\Rightarrow$  $e=\frac{3}{5}$

Option C is the answer.
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