Conic Sections Question 333
Question: If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is
Options:
A) 3
B) $ 4\sqrt{2} $
C) 6
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{a}{e}-ae=8 $ . Also $ e=\frac{1}{2} $
therefore $ a=\frac{8e}{(1-e^{2})}=\frac{8.4}{2(3)}=\frac{16}{3} $
$ \therefore b=\frac{16}{3}\sqrt{( 1-\frac{1}{4} )}=\frac{16}{3}\frac{\sqrt{3}}{2}=\frac{8\sqrt{3}}{3} $
Hence the length of minor axis is $ \frac{16\sqrt{3}}{3} $ .
BETA
