A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) None of these
Correct Answer: B
Solution :
[b] Let \[P\left( \sqrt{6}cos\theta ,\text{ }\sqrt{2}sin\theta \right)\] be a point on the ellipse \[\frac{{{x}^{2}}}{6}+\frac{{{y}^{2}}}{2}=1\] in the first-quadrant \[\left( 0<\theta <\frac{\pi }{2} \right)\] \[C{{P}^{2}}=6co{{s}^{2}}\theta +2si{{n}^{2}}\theta =4\] \[\Rightarrow 2+4co{{s}^{2}}\theta =4\] \[\Rightarrow co{{s}^{2}}\theta =\frac{1}{2}\] \[\Rightarrow cos\theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}\]
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