JEE MAIN - Mathematics (2008 - No. 16)
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 :
$${{8 \over 3}}$$
$${{2 \over 3}}$$
$${{4 \over 3}}$$
$${{5 \over 3}}$$
Explanation
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 $$=8/3$$
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