Jak vypočítat Ellipse
Co je Ellipse?
An ellipse is an oval curve defined by two focal points. It has two axes: the semi-major axis (a, longer) and semi-minor axis (b, shorter). Ellipses appear in planetary orbits, optics, and engineering.
Vzorec
Area = πab; Perimeter ≈ π[3(a+b) − √((3a+b)(a+3b))]; e = √(1 − (b/a)²)
- a
- semi-major axis (half long axis) (length)
- b
- semi-minor axis (half short axis) (length)
- e
- eccentricity — measure of how "stretched" the ellipse is
Průvodce krok za krokem
- 1Area = π × a × b
- 2Perimeter ≈ π × [3(a+b) − √((3a+b)(a+3b))] (Ramanujan)
- 3Eccentricity = √(1 − (b/a)²)
- 4A circle is an ellipse where a = b
Worked Examples
Vstup
a = 5, b = 3
Výsledek
Area = π×5×3 = 47.12, Eccentricity ≈ 0.8
Vstup
a = 10, b = 6
Výsledek
Area = 188.5, Perimeter ≈ 51.05
Frequently Asked Questions
What is eccentricity and what does it measure?
Eccentricity (e) measures how much the ellipse deviates from a circle. e=0 is a circle, e approaching 1 is very stretched.
How do I calculate the foci of an ellipse?
The distance from center to each focus is c = √(a² − b²). The foci lie on the major axis.
Why is the perimeter approximate?
Unlike circles, ellipse perimeter has no simple closed formula. Ramanujan's approximation is highly accurate.
Jste připraveni počítat? Vyzkoušejte bezplatnou kalkulačku Ellipse
Zkuste to sami →