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 [IIT Screening 2003]

Tangent is drawn to ellipse \[\frac{{{x}^{2}}}{27}+{{y}^{2}}=1\] at \[

1.	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 [IIT Screening 2003]
A.	\[\pi /3\]
B.	\[\pi /6\]
C.	\[\pi /8\]
D.	\[\pi /4\]
Answer» C. \[\pi /8\]

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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 [IIT Screening 2003]

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