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upendra hembram Grade: 12
        

find the greastest area of the rectangle which can be inscribed in the ellipse; x2/a2+y2/b2=1 with sides parallel to the co-ordinate axes


 

7 years ago

Answers : (2)

aman walia
24 Points
										

let the vertices of  rectangle be (asinø,bcosø),(asinø,-bcosø),(-asinø,-bcosø),(-asinø,bcosø).(in clockwise sense)


 


then area of rectangle =2absin2ø


 


d(area)/dø=2abcosø;


 


for(maxima) 2ab cosø=0


 


so ø=pi/4


 


also d2a/dø2  <0for(ø=pi/4)


 


hence area =2ab


 

7 years ago
aman walia
24 Points
										

let the vertices of  rectangle be (asinø,bcosø),(asinø,-bcosø),(-asinø,-bcosø),(-asinø,bcosø).(in clockwise sense)


then area of rectangle =2absin2ø


d(area)/dø=2abcosø;


for(maxima) 2ab cosø=0


so ø=pi/4


also d2a/dø2  <0for(ø=pi/4)


hence area =2ab


7 years ago
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