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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Ellipse
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[Post New]10 Mar 2008 16:43:06 IST
    Subject: Ellipse
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pantpranav (367)

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Find the area of the greatest rectangle that can be inscribed in the following ellipse :
x2/a2 + y2/b2 = 1.


    
[Post New]10 Mar 2008 16:52:48 IST
    Subject: Re:Ellipse
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akhil_o (2709)

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let the vertice in the positive quadrant be (p,q)
for forming a rectangle others are
(-p,q),(p,-q),(-p,-q)

area=2p*2q..it will be clearer with a figure..
A=4pq

but p2/a2+q2/b2=1
b2p2+q2a2=a2b2
q2=b2(a2-p2)
q= b2(a2-p2)

A=4p b2(a2-p2)
differentiating wrt p and equating to zero for maxima
we have
4p2b=4b(a2-p2)
or
2p2=a2
p=a/ 2

q=b/ 2
A=4pq=4ab/2
hence area max-2ab
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[Post New]10 Mar 2008 17:02:37 IST
    Subject: Re:Ellipse
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pantpranav (367)

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This is also correct.
I'm sure you'll crack IIT.


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