Conic Sections Question 271
Question: The distance between the directrices of the ellipse $ \frac{x^{2}}{36}+\frac{y^{2}}{20}=1 $ is
Options:
A) 8
B) 12
C) 18
D) 24
Show Answer
Answer:
Correct Answer: C
Solution:
$ a=6,\ b=2\sqrt{5} $
$ b^{2}=a^{2}(1-e^{2}) $
therefore $ \frac{20}{36}=(1-e^{2}) $
therefore $ e=\sqrt{\frac{16}{36}}=\frac{2}{3} $
But directrices are $ x=\pm \frac{a}{e} $
Hence distance between them is 2. $ \frac{6}{2/3}=18 $ .
BETA
