Multivaraible Calc. vectors

ok..so here is what I am given for this problem:

The vector function r sends a point (u,v) in the plane to a point (vector) in R3.

r(u,v)= (1/2sqrt(v)*cosh U, sqrt(V)*sinhU, V)

or in other words:

x= 1/2sqrt(V)*coshU

y= sqrt(V)*sinhU

z=V

these points satisfy the equation: z= 4x^2-y^2, and it is a hyperbolic parabloid.

Question:

Fix u=u(sub 0) and consider the parametised curve r(sub v), defined as rv(v)=r(u(sub )), v)

Write explicitly r(subv)(v):

What does this mean? does it mean to replace all u with u(sub 0) in the original vector equation? Help..please someone explain this to me.