AdvancedConics
Hyperbola
x²/a² − y²/b² = 1
Overview
A hyperbola is the set of points where the difference of distances to two foci is constant.
Domain
(-∞, -a] ∪ [a, +∞)
Range
(-∞, +∞)
Key Properties
1
Two separate branches
2
Asymptotes: y = ±(b/a)x
3
Foci at (±c, 0) where c² = a² + b²
4
Opens left/right (x² term positive) or up/down (y² term positive)
Key Insight
Hyperbolas describe the path of objects in gravitational slingshots and some comet orbits.
Visualize Hyperbola
Interact with the graph and explore this curve in the analytic geometry visualizer.