# Maximum Parallelogram Area within an Ellipse

Calculus Level 4

Given the ellipse:

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

Two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are chosen on it. A parallelogram is drawn using the points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ and $$(-x_1, -y_1)$$ and $$(-x_2, -y_2)$$. What is the maximum area of this parallelogram ?

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