I think the problem answer is incorrect.
The area is pi*a*b for a standard ellipse (x^2/a^2 + y^2/b^2 = 1)
and not the one that is mentioned. So according to the problem statement, the answer should be pi*sqrt(a*b)
Thank you Dyuman.
I missed the terms of the square.
I modified the form of the ellipse equation.
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