I don't know how to draw or visualize the hyperbola with the below information. Would love a step by step guide if possible.

Sketch the hyperbola, showing the asymptotes, the point P and the tangent at P.

The Hyperbola is in R^2.

It is described by the below parametric equations.

x = sec t, y = 2 tan t (t ∈ (-π/2 , π/2) U ( π/2 , (3π)/2)

The coordinates of point P, where t = π/3, are ( 2 , 2*sqrt3)

y = (((4rt3)(x))/3) - ((2rt3)/3) is the equation of the tangent line.

the asymptotes are