Hyperbola: x²/a² − y²/b² = 1 (horizontal). Asymptotes: y = ±(b/a)x. Eccentricity e = c/a where c = √(a²+b²), always e > 1. Foci at (±c,0). Difference of distances to foci = 2a for any point on the hyperbola.
How to Use
Enter parameters:
- a: Transverse semi-axis
- b: Conjugate semi-axis
- Orientation: Horizontal or vertical
Asymptotes
As |x|→∞, the hyperbola approaches y = ±(b/a)x. The asymptotes form a cross at the center, guiding the shape of the curve.
Applications
GPS/LORAN navigation (time difference → hyperbola), sonic boom patterns, shadow curves, and particle physics (Rutherford scattering).
Step-by-Step Instructions
- 1Enter semi-axis a.
- 2Enter semi-axis b.
- 3Choose orientation.
- 4View asymptotes.
- 5Check foci and eccentricity.