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If the area of a square circumscribing a...

If the area of a square circumscribing an ellipse is 10 square units and maximum distance of a normal from the centre of the ellipse is 1 unit, than find the eccentricity of ellipse

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The correct Answer is:
`sqrt((3)/(4))`
Area of the circumscribing is `2(a^(2)+b^(2))` (using director circle concept)
`rArr 2(a^(2)+b^(2))=10`
`rArra^(2)+b^(2)=5" "(1)`
Also, maximum distance of a normal from centre is 1.
`:. (a-b)=1" "(2)`
From (1) and (2) , we have
ab=2 and a+b=3
Solving, we get a=2, b=1
`:. e=sqrt((3)/(4))`
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