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Question

If the ellipse x2a2+y2b2=1 is inscribed in a rectangle whose length to breadth ratio is 2:1, then the area of the rectangle is

A
4.(a2+b2)7
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B
4.(a2+b2)3
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C
12.(a2+b2)5
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D
8.(a2+b2)5
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Solution

The correct option is B 8.(a2+b2)5
l=2a
b=2b
l:b=2:1lb=212a2b=21a=2b=b
Area=l×b =2a×a =2a2
OR
=l×b
=4b×2b
=8b2
Now using option D
Area=8(a2+b2)5=8(4b2+b2)5=8×5b25
Area=8b2
Answer is D.

668008_117703_ans_0472d86ee5354caf96b4cea774331a53.png

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