+1678 The equation of an ellipse is
\[\frac{x^2}{4} + y^2 = 1.\]
Let $C$ be a point that varies on this ellipse, and let $H$ be the orthocenter of triangle $ABC,$ where $A = (-4,0)$ and $B = (4,0).$ Then $H$ traces a closed curve as $C$ varies over the ellipse. Find the area inside the closed curve.
