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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Aicharya · Accepted Answer

Major axis is along $x$-axis. $ \begin{aligned} & \frac{a}{e}-a e=4 \ & a\left(2-\frac{1}{2}ight)=4 \ & a=\frac{8}{3} . \end{aligned} $

A focus of an ellipse is at the origin. The directrix is the line $x=4$ and the eccentricity is $1 / 2$.…