Conic Sections Question 388
Question: Eccentricity of the ellipse $ 4x^{2}+y^{2}-8x+2y+1=0 $ is
Options:
A) $ 1/\sqrt{3} $
B) $ \sqrt{3}/2 $
C) $ 1/2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ 4x^{2}-8x+y^{2}+2y+1=0 $
therefore $ {{(2x-2)}^{2}}+{{(y+1)}^{2}}=-1+4+1 $
therefore $ \frac{{{(x-1)}^{2}}}{1}+\frac{{{(y+1)}^{2}}}{4}=1 $
therefore $ e=\sqrt{1-\frac{1}{4}} $
therefore $ e=\frac{\sqrt{3}}{2} $ .
BETA
