Any point on x^2/a^2 - y^2/b^2 = 1 is P(theta) = (asec(theta), btan(theta)). This uses the identity sec^2(theta) - tan^2(theta) = 1. The parameter theta is the eccentric angle, defined via the auxiliary circle. For the right branch, -pi/2 < theta < pi/2; for the left branch, pi/2 < theta < 3pi/2. An alternative parametric form uses the hyperbolic functions: (acosh(t), b*sinh(t)).