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If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8 , then the eccentricity is
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Verified Answer
The correct answer is:
$\frac{3}{5}$
Here, $2 a e=6$ and $2 b=8 \Rightarrow b=4$
$\begin{aligned}
& b^2=16 \\
& \Rightarrow \quad a^2\left(1-e^2\right)=16 \\
& \Rightarrow \quad \frac{9}{e^2}\left(1-e^2\right)=16 \\
& \Rightarrow \quad 9-9 e^2=16 e^2 \\
& \Rightarrow \quad 25 e^2=9 \\
&
\end{aligned}$
$\Rightarrow \quad e=\frac{3}{5}$
$\begin{aligned}
& b^2=16 \\
& \Rightarrow \quad a^2\left(1-e^2\right)=16 \\
& \Rightarrow \quad \frac{9}{e^2}\left(1-e^2\right)=16 \\
& \Rightarrow \quad 9-9 e^2=16 e^2 \\
& \Rightarrow \quad 25 e^2=9 \\
&
\end{aligned}$
$\Rightarrow \quad e=\frac{3}{5}$
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