Hi all, I've recently bought a few maths books to study in my spare time and I'm stuck on the below question. I've found the point P and I think the equation of the tangent is y = (4rt3)(x) - 2rt3. I have no idea how to find the equations of the asymptotes.

This question is about a Hyperbola 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)

The gradient of the tangent to the hyperbola at the point with parameter t is 2/sin t, where t is not equal to 0 or π. Using this information, ﬁnd the equation of the tangent to the hyperbola at the

point P.

Find the equations of the asymptotes of the hyperbola

So could someone please confirm my answer, for the equation of the tangent and how to get the equations of the asymptotes?

Thanks