Hyperbola Calculator
Compute eccentricity, foci, vertices and asymptotes of a hyperbola from a and b.
Inputs
Eccentricity
1.166190
Focal Distance (c)
5.8310units
Vertex (±a)
5.0000units
Asymptote Slope (±b/a)
0.6000
Step by step
Focal distance
c = √(5² + 3²) = √34
= 5.8310
Eccentricity
e = c/a = 5.8310/5
= 1.166190
Asymptote slopes
y = ±(3/5)x = ±0.6000x
How it works
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.
Formulas
Focal Distance
c = √(a² + b²)
- a
- Semi-transverse axis
- b
- Semi-conjugate axis
Eccentricity
e = c / a
- c
- Focal distance
- a
- Semi-transverse axis
Frequently Asked Questions
How is a hyperbola different from an ellipse?
An ellipse has c² = a² − b² (e < 1), while a hyperbola has c² = a² + b² (e > 1). A hyperbola has two separate branches.
What are the asymptotes?
The lines y = (b/a)x and y = −(b/a)x that the hyperbola approaches but never touches.