Ellipse Focus Triangle Area Calculator & Formula Analysis

Precision Note: Results rounded to 4 decimal places for educational reference.

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Historical Origins & Formula Derivation

The area of an ellipse focus triangle is derived from geometric properties of ellipses. The formula used here is:
Area \( S = b^2 \cdot \cot\left(\frac{\theta}{2}\right) \)
where \( b \) is the short semi-axis length, and \( \theta \) is the eccentricity angle (in radians, \( 0 < \theta < \frac{\pi}{2} \)).

Ellipse focus triangle diagram