A focus of an ellipse is at the origin. The directrix is the line x=4 and the eccentricity is \[{{1 \over 2}}\]. Then the length of the semi-major axis is :
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Official solution
Perpendicular distance of directrix from focus
\[ = {a \over e} - ae = 4\]
\[ \Rightarrow a\left( {2 - {1 \over 2}} \right) = 4\]
\[ \Rightarrow a = {8 \over 3}\]
\[\therefore\] Semi major axis =8/3