Question 6 - A-Level Maths

The hyperbola $H$ is given by the equation $x ^ { 2 } - y ^ { 2 } = 1$
1. Write down the equations of the two asymptotes of $H$.
2. Show that an equation of the tangent to $H$ at the point $P ( \cosh t , \sinh t )$ is
$$y \sinh t = x \cosh t - 1$$ The tangent at $P$ meets the asymptotes of $H$ at the points $Q$ and $R$.
Show that $P$ is the midpoint of $Q R$.
Show that the area of the triangle $O Q R$, where $O$ is the origin, is independent of $t$.