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find the greastest area of the rectangle which can be inscribed in the ellipse; x 2 /a 2 +y 2 /b 2 =1 with sides parallel to the co-ordinate axes

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


 

Grade:12

2 Answers

aman walia
24 Points
11 years ago

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

 

aman walia
24 Points
11 years ago

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


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