The Hyperbola

Differences and asymptotes

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A hyperbola: points where $|d_1 - d_2| = 2a$ (constant).
• $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, with $c^2 = a^2 + b^2$ and asymptotes $y = \pm\frac{b}{a}x$.
• Unbound orbits are hyperbolas. Time differences locate objects on hyperbolas.

Steps

1. A constant difference
2. Foci of a hyperbola
3. Flybys
4. Finding a ship
5. A hyperbola’s eccentricity
6. Asymptotes