Hyperbola

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A hyperbola is a type of conic section. It is defined as the set of all points for which the difference in the distance to two fixed points (foci) is constant. At large distances from the vertices the hyperbola begins to approximate two lines, known as asymptotes.

http://www.sisweb.com/math/graphs/conics/cone-hyp.jpg

Equations (Cartesian):

  ((x-a)/c)2 - ((y-b)/d)2 =  1
  ((x-a)/c)2 - ((y-b)/d)2 = -1
  y-a =  c/(x-b)
  y-a = -c/(x-b)

Equations (Polar):

  r^2 =  a sec 2t
  r^2 = -a sec 2t
  r^2 =  a csc 2t
  r^2 = -a csc 2t