# Maximum Triangle Area within an Ellipse

**Geometry**Level 3

Given the ellipse:

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

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