Question

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

• A. $\frac{5}{3}$
• B. $\frac{8}{3}$
• C. $\frac{2}{3}$
• D. $\frac{4}{3}$

Answer 1

Answer: (B)

$\frac{8}{3}$

Focus of ellipse is at origin.

Directrix $x=4$ and $e=\frac{1}{2}$

Major axis is along x-axis.

$\Rightarrow \frac{a}{e}-ae=4$

$\Rightarrow \frac{a}{\frac{1}{2}}-\frac{a}{2}=4$

Using value of $e$ we get $a=\frac{8}{3}$