Hyperbola:

set of points whose difference of distances d1-d2 to two foci F1,F2 are the same.
Hyperbolas centered at origin (0,0): f=√(a2+b2)    e=f/a
  

"Unit hyperbola":

  
     
  

Hyperbola centered at (h,k):

Distance from center to focus F is c=√(a2+b2)
The eccentricity e=c/a, e>1.