Conic Sections Question 382
Question: In the ellipse, minor axis is 8 and eccentricity is $ \frac{\sqrt{5}}{3} $ . Then major axis is
[Karnataka CET 2002]
Options:
A) 6
B) 12
C) 10
D) 16
Show Answer
Answer:
Correct Answer: B
Solution:
Given, minor axis of ellipse $ (2b)=8 $ or $ b=4 $ and eccentricity $ (e)=\sqrt{5}/3 $ .
We know that in an ellipse, $ e^{2}=1-\frac{b^{2}}{a^{2}} $ or $ \frac{5}{9}=1-\frac{16}{a^{2}} $ or $ \frac{16}{a^{2}}=1-\frac{5}{9} $ or $ a^{2}=\frac{16\times 9}{4} $
$ =36 $ or $ a=6. $ We also know that major axis of the ellipse $ =2a=2\times 6=12. $
BETA
