What is c for a hyperbola?
c = √(a²+b²), the distance from center to each focus.
Hyperbola Calculator
Analyze a horizontal transverse-axis hyperbola given center and a, b.
Enter hyperbola parameters
Provide h, k, a > 0, and b > 0 for the standard horizontal form.
About this calculator
How to use Hyperbola Calculator, plus the formulas and logic behind the results.
Tool description
For (x−h)²/a² − (y−k)²/b² = 1, c = √(a²+b²), eccentricity e = c/a > 1, and asymptotes are y−k = ±(b/a)(x−h).
How to use
- Enter center (h,k).
- Enter positive a and b.
- Select Calculate.
- Review c, e, foci, vertices, and asymptotes.
Formulas & reference
c = √(a² + b²)e = c/aFoci: (h±c, k)Asymptotes: y − k = ±(b/a)(x − h)
Hyperbola facts
- e > 1 for every hyperbola
- c² = a² + b²
- Vertices at (h±a, k)
- Asymptotes pass through the center
Calculation logic
Applies standard horizontal transverse-axis hyperbola identities with π unused.
This form opens left/right. Vertical transverse axis is a different standard form.
Hyperbola Calculator FAQ
Common questions about this calculator and how to use the results.
What is eccentricity?
e = c/a. For hyperbolas, e > 1.
Where are the foci?
At (h±c, k) for this horizontal form.
What are the asymptotes?
The lines y−k = ±(b/a)(x−h).
Must a and b be positive?
Yes in this calculator.
Does this cover vertical hyperbolas?
No—this tool is for the horizontal transverse-axis equation shown.