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The ratio of the areas of two regions of...

The ratio of the areas of two regions of the curve `C_(1)-=4x^(2)+pi^(2)y^(2)=4pi^(2)` divided by the curve `C_(2)-=y=-(sgn(x-(pi)/(2)))cosx` (where sgn (x) = signum (x)) is

A

`(pi^(2) - 2)/(pi^(2) + 2)`

B

`(pi^(2) + 4)/(pi^(2) - 2 sqrt(2))`

C

`(pi^(2) + 6)/(pi^(2) + 3 sqrt(2))`

D

`(pi^(2) + 1)/(pi^(2) - sqrt(2))`

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The correct Answer is:
A
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