Conic Sections Question 143
Question: Eccentric angle of a point on the ellipse $ x^{2}+3y^{2}=6 $ at a distance 2 units from the centre of the ellipse is
[WB JEE 1990]
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{\pi }{3} $
C) $ \frac{3\pi }{4} $
D) $ \frac{2\pi }{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the eccentric angle of the point be $ \theta $ , then its co-ordinates are $ (\sqrt{6}\cos \theta ,\sqrt{2}\sin \theta ). $
Hence $ 6{{\cos }^{2}}\theta +2{{\sin }^{2}}\theta =4 $ or $ {{\cos }^{2}}\theta =\frac{1}{2} $
Hence, $ \cos \theta =\pm \frac{1}{\sqrt{2}} $ ,$ \theta =\frac{\pi }{4} $ or $ \frac{3\pi }{4} $ .
BETA
