A) \[\frac{{{a}^{2}}+{{b}^{2}}}{2}\]
B) \[\frac{{{(a+b)}^{2}}}{2}\]
C) ab
D) \[\frac{{{(a-b)}^{2}}}{2}\]
Correct Answer: C
Solution :
Equation of tangent at \[(a\cos \theta ,\ b\sin \theta )\] is \[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\] \[P=\left( \frac{a}{\cos \theta },\,0 \right)\] \[Q=\left( 0,\,\frac{b}{\sin \theta } \right)\] Area of \[OPQ=\frac{1}{2}\left| \,\left( \frac{a}{\cos \theta } \right)\,\left( \frac{b}{\sin \theta } \right)\, \right|=\frac{ab}{|\sin 2\theta |}\] \ \[{{(\text{Area})}_{\min }}=ab\].You need to login to perform this action.
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