In the coordinate plane, let A = (-2,0) and B = (2,0) Let C be a variable point on the ellipse \frac{x^2}{4} + y^2 = 1
and let H be the orthocenter of triangle ABC As C varies on the ellipse, the point H traces a curve. Find the area inside the curve.
+9519 I have made a GeoGebra simulation of the problem, and it appears that the curve that H traces is an ellipse with major axis 4 units and minor axis 2 units.
GeoGebra simulation: https://www.geogebra.org/calculator/my8uamwy
Therefore, the area inside the curve is \(\pi \cdot 4 \cdot 2 = 8\pi\text{ square units}\).
