Question

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be ½, then length of the minor axis is

• A. 3
• B. 4$\sqrt{2}$
• C. 6
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\frac{a}{e}$- ae = 8. Also e = $\frac{1}{2}$⇒ a = $\frac{8e}{\left( 1 - e^{2} \right)} = \frac{8.4}{2(3)} = \frac{16}{3}$

∴b = $\frac{16}{3}\sqrt{\left( 1 - \frac{1}{4} \right)} = \frac{16}{3}\frac{\sqrt{3}}{2} = \frac{8\sqrt{3}}{3}$Hence the length of minor axis is $\frac{1}{2}$.