x = a sec θ and y = b tan θ satisfy equation x²/a² - y²/b² = 1 as the transformation turns out to be sec² θ - tan² θ which is equal to 1.
Hence the parametric coordinates of hyperbola are (a sec θ,b tan θ) and x = a sec θ and y = b tan θ are called parametric equations of hyperbola.
x = a cosh θ and y = a sinh θ are also parametric equations of hyperbola.
cosh θ = (eθ+e-θ)/2
sinh θ = (eθ-e-θ)/2