I tried in the first place to use the effective potential of a parabolic orbit which is 0 to get the angular momentum L.
Evaluating the function U(r) at r = rP i get U(rP) = L^2/(2m(rP)^2) - GmM/rP = 0.
Here I get L = m√(2GMrP).
Now the relationship between angular momentum L and areal...