Tangent is drawn to ellipse $\frac{{{x^2}}}{{27}} + {y^2} = 1\,at\,(3\sqrt 3 \cos \theta ,\sin \theta )$ where $\theta \in (0, \pi /2)$ . Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is minimum, is
Tangent is drawn to ellipse $\frac{{{x^2}}}{{27}} + {y^2} = 1\,at\,(3\sqrt 3 \cos \theta ,\sin \theta )$ where $\theta \in (0, \pi /2)$ . Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is minimum, is
- A
$\pi /3$
- B
$\pi /6$
- C
$\pi /8$
- D
$\pi /4$
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