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Offline Centres

A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $\frac{1}{2}$ The length
of semi-major axis is

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$\frac{8}{3}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{5}{3}$

answer is A.

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Detailed Solution

Let C be the centre.

$\begin{array}{l} C X = \frac{a}{e}, C S = a e \\ ∴ S X = 4 = \frac{a}{e} - a e = 2 a - \frac{a}{2} = \frac{3 a}{2} \\ ∴ a = \frac{8}{3} . \end{array}$

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