A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{3\pi }{4}\]
D) \[\frac{2\pi }{3}\]
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 \[\frac{3\pi }{4}\].
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