Can someone please explain to me why the parametric coordinates $\displaystyle \

(a\cosh t,a\sinh t)

\$ can only represent one branch of the rectangular hyperbola with the equation $\displaystyle \

x^2 + y^2 = a^2

\$, and what would the parametric coordinates of the other branch be?

I'm stuck on a question relating to the rectangular hyperbola, which is:

The normal at $\displaystyle \

P(a\cosh t,a\sinh t)

\$, where t>0, passes through the point $\displaystyle \

(4a,0)

\$. Find the non-zero value of t, giving your answer as a natural logarithm.

I must admit I have absolutely no idea how to even begin the question. Can someone please enlighten me?