question_answer

Normal is drawn to the ellipse \[\frac{{{x}^{2}}}{27}+{{y}^{2}}=1\] at a point \[\left( 3\sqrt{3}cos\theta ,\sin \theta  \right)\]where \[0<\theta <\frac{\pi }{2}\]. The value of \[\theta \] such that the area of triangle formed by normal and coordinate axes is maximum, is

A)  \[\frac{\pi }{8}\]                             

B)  \[\frac{\pi }{6}\]

C)  \[\frac{\pi }{4}\]                                             

D)  \[\frac{\pi }{3}\]