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P5 Topic 1: Coordinate Systems
The hyperbola 2 backmore
Move point d left and right to view the hyperbola that has an eccentricity equal to the x coordinate of d.


Summary

  • the two green curves together are a hyperbola
  • the point f is a focus of the ellipse, and the red line is a directrix of the ellipse.
  • the eccentricity, e, is given by the x-coordinate of d. The coordinates of f are (e,0). The directrix is at x = 1/e
  • all hyperbolas have an eccentricity greater than 1
  • the hyperbola with an eccentricity of V¯2 is called a rectangular hyperbola. The rectangular hyperbola is notable because it has several very simple mathematical equations.
  • all hyperbolas have an eccentricity greater than 1
  • Typically, a hyperbola has equation:hyperbola
  • Its eccentricity, e, is found from: hyperbola eccentricity
  • The directrices are at: hyperbola directrices
  • The foci are at (±ae,0)
  • The asymptotes are hyperbola asymptotes
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