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A focus of an ellipse is at the origin. The directrix is the line $x=4$ and the eccentricity is $1 / 2$. Then the length of the semi-major axis is
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Verified Answer
The correct answer is:
$\frac{8}{3}$
$\frac{8}{3}$
Major axis is along $x$-axis.
$$
\begin{aligned}
& \frac{a}{e}-a e=4 \\
& a\left(2-\frac{1}{2}\right)=4 \\
& a=\frac{8}{3} .
\end{aligned}
$$
$$
\begin{aligned}
& \frac{a}{e}-a e=4 \\
& a\left(2-\frac{1}{2}\right)=4 \\
& a=\frac{8}{3} .
\end{aligned}
$$
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