Area of a Region

Calculus Level 4

The area enclosed by the curve \(4x^2 + 12xy + 9y^2 + 8\sqrt{13} x + 12\sqrt{13}y - 65 = 0 \) on the interval \(-a \leq x \leq a \) for \(a>0\), can be expressed as \( m * \sqrt{n} * a\), where \(m\) and \(n\) are coprime positive integers.

Find \(m+n\).


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