Hyperbolas

Math

Definition

A conic section formed by the set of all points where the absolute difference of distances to two fixed points (foci) is constant. A hyperbola has two separate curved branches that open either horizontally or vertically, with asymptotes guiding their shape.

Examples

  • The path of a spacecraft doing a gravitational slingshot around a planet
  • The shape formed by the shadow of a lampshade on a wall
  • LORAN navigation systems use intersecting hyperbolas to determine position
Key Fact

Standard form: (x−h)²/a² − (y−k)²/b² = 1 (horizontal) or (y−k)²/a² − (x−h)²/b² = 1 (vertical)

Related Terms

Ellipses Parabolas Identifying conics Asymptotes

Study This Concept

Practice hyperbolas with free review games in these units:

Pre-Calculus Unit 8: Conic Sections