📐Hyperbola Calculator (x²/a² - y²/b² = 1)
A hyperbola is the set of points where the difference of distances to two foci is constant. Standard form: x²/a² − y²/b² = 1. It has two branches and asymptotes y = ±(b/a)x.
- 1c = √(a²+b²) — focal distance
- 2Eccentricity e = c/a > 1
- 3Latus rectum: 2b²/a
- 4Asymptotes: y = ±(b/a)x
a=3, b=4=c=5 · e=5/3≈1.67 · Asymptotes y=±4x/33-4-5 Pythagorean triple
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Fun Fact
Hyperbolas appear in Rutherford's gold foil experiment (alpha particle scattering) and the trajectory of interstellar object 'Oumuamua.
References
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