Compute eccentricity, foci, vertices and asymptotes of a hyperbola from a and b.
For the standard hyperbola x²/a² − y²/b² = 1, the foci are at (±c, 0) where c = √(a²+b²). Eccentricity e = c/a is always > 1. Asymptotes are y = ±(b/a)x.
Focal Distance
c = √(a² + b²)
Eccentricity
e = c / a
An ellipse has c² = a² − b² (e < 1), while a hyperbola has c² = a² + b² (e > 1). A hyperbola has two separate branches.
The lines y = (b/a)x and y = −(b/a)x that the hyperbola approaches but never touches.