A) \[\frac{a}{b}\]
B) \[\sqrt{ab}\]
C) \[ab\]
D) \[2ab\]
Correct Answer: D
Solution :
The parametric coordinates of a point that lies on an ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}\,+\frac{{{y}^{2}}}{{{b}^{2}}}\,=1\] are \[(a\cos \theta ,\,b\sin \theta )\]. Let the coordinates of the vertices of rectangle ABCD be andthen Length of rentann and breadth of rectangle, Area of rectangle. Area of rectangle, ...(i) \[\therefore \,\,\frac{dA}{d\theta }=2\times 2\,\,ab\,\cos \,2\theta \,\Rightarrow \,\frac{dA}{d\theta }=0\] For maxima or minima, put Now, Now, Area is maximum at Maximum area of rectangle =2 ab sq units [from Eq. (i)] Alternate Solution From Eq. (i), Area of rectangle, and A is maximum when Maximum area of rectanglesq unitsYou need to login to perform this action.
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