What are the parametric equations of a hyperbola?

Answer 1

x = a cosh(t)

y = a sin(t)

gives the right side of the hyperbola.

x = -a cosh(t)

y = a sin(t)

gives the left side of the hyperbola.

where t ranges over R

sinh(t) = (et - e-t)/2

cosh(t) = (et + e-t)/2