A) 9
B) \[\frac{9}{2}\]
C) \[9\sqrt{3}\]
D) \[3\sqrt{3}\]
Correct Answer: A
Solution :
Let \[P(3\sqrt{3}\cos \theta ,\sqrt{3}\sin \theta )\] \[\therefore \]tangent is\[\frac{x}{3\sqrt{3}}\cos \theta +\frac{y}{\sqrt{3}}\sin \theta =1\] \[\Rightarrow \]\[A(3\sqrt{3}\sec \theta ,0)\] \[B(0,\sqrt{3}\sec ec\theta )\] \[\therefore \]Area of \[\Delta OAB=\frac{1}{2}OA.OB\] \[=\frac{1}{3}(3\sqrt{3}\sec \theta .\sqrt{3}\cos ec\theta )\] \[=\frac{9}{2\sin \theta \cos \theta }=\frac{9}{\sin 2\theta }\] \[\therefore \]minimum area of \[\Delta OAB=\frac{9}{1}=9\]You need to login to perform this action.
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