A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
Correct Answer: C
Solution :
Given equation of an ellipse is \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1\] and point \[P(2,\sqrt{3})\] Let \[\theta \] be the eccentric angle. The parametric coordinate of an ellipse is \[\left. \begin{matrix} x=4\,\cos \theta \\ y=2\sin \theta \\ \end{matrix} \right\}\] ……(i) Given that, eccentric angle at P is, \[2=4\,\cos \theta \Rightarrow \cos \theta =\frac{1}{2}\] \[\sqrt{2}=2{{\sin }^{\theta }}\Rightarrow \sin \theta =\frac{\sqrt{3}}{2}\] Hence, \[\theta =\frac{\pi }{3}\]You need to login to perform this action.
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