Ellipse: x²/a² + y²/b² = 1. Area = πab. Eccentricity e = √(1−b²/a²) where a≥b. Foci at (±c,0) where c = ae. Perimeter ≈ π[3(a+b)−√((3a+b)(a+3b))] (Ramanujan). A circle is an ellipse with e=0.
How to Use
Enter semi-axes:
- a: Semi-major axis
- b: Semi-minor axis
- Output: All ellipse properties
Eccentricity
- e = 0: circle
- 0 < e < 1: ellipse
- e = 1: parabola
- e > 1: hyperbola
In Astronomy
Planets orbit in ellipses (Kepler's 1st Law). Earth's orbit has e ≈ 0.017 (nearly circular). Mercury: e ≈ 0.206 (most eccentric planet).
Step-by-Step Instructions
- 1Enter semi-major axis a.
- 2Enter semi-minor axis b.
- 3View area and perimeter.
- 4Check eccentricity.
- 5Find foci locations.