Maximum Triangle Area within an Ellipse

Geometry Level 3

Given the ellipse:

x2a2+y2b2=1 \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

where a>0 a > 0 and b>0 b > 0 , three points (x1,y1) (x_1, y_1) , (x2,y2) (x_2, y_2) , and (x3,y3) (x_3, y_3) are chosen to lie on it. What is the maximum area of the triangle formed by these three points?

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