Example 1
\(a = 5, b = 3 \rightarrow A = 47.12\) sq units
Ellipsen-Rechner
Berechnen Sie Fläche, Umfang und Exzentrizität einer Ellipse mit interaktiver Visualisierung der Haupt- und Nebenachsen
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
An ellipse is a closed curve where the sum of distances from any point on the curve to two fixed points (foci) is constant. It has two perpendicular axes: the major axis (longer) and the minor axis (shorter).
Key properties:
- Area: A = π × a × b
- Perimeter: No exact formula; use Ramanujan's approximation
- Eccentricity: e = √(1 - b²/a²), where 0 ≤ e < 1
- Foci distance: c = a × e from center along major axis
- When a = b, the ellipse becomes a circle
- Standard equation: x²/a² + y²/b² = 1
\(A = \pi ab\)
Worked Examples
Example 2
\(a = 8, b = 6 \rightarrow A = 150.80\) sq units