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Area of the greatest rectangle that can be inscribed in the ellipse   \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1   is

Option: 1

ab\; \;


Option: 2

\; 2ab\; \;


Option: 3

\; a/b\; \;


Option: 4

\; \sqrt{ab}


Answers (1)

best_answer

As we have learned

Introduction of area under the curve -

The area between the curve y= f(x),x axis and two ordinates at the point  x=a\, and \,x= b\left ( b>a \right ) is given by

A= \int_{a}^{b}f(x)dx=\int_{a}^{b}ydx

- wherein

 

 

Area

2 a \cos \theta \times 2b \sin \theta \\ = 4 ab \sin \theta \cos \theta \\ = 2 ab \sin 2 \theta 

Area greatest = 2ab 

Where \theta = \pi /4

 

 

 

Posted by

Rishi

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