⃗r : U → R3 ,U ⊂ R 2

We are given:

⃗r (u,v)= (√v/2 cosh u, √v2sinhu,v)

or the same as:

x= √v/2 cosh u

y- √vsinh u

z=u

The question is verify that the points r(u,v) satisfy the equation z= 4x^2-y^2. And identify what kind of surface z=4x^2-y^2 is.

This is what I did:

I identified the surface given by the equation z=4x^2-y^2 as a hyperbolic parabloid.

The part I am confused about is showing that it satisfies the equation. what I did is substituted the given values of x,y,and z into this formula, and I got:

v= vcsosh^2u-sin^2u

I don't know where to go from here, would appreciate any suggestions.