# 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 $$\dfrac m{\sqrt n} a$$, where $$m$$ and $$n$$ are coprime positive integers.

Find $$m+n$$.

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