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Math Help - Vector function of two arguments

  1. #1
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    Vector function of two arguments

    ⃗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.
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  2. #2
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    Joined
    Oct 2008
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    Hi,

    the way you worte it looks a little confusing.

    so as far as I understind is:

    x=SQRT(v/2)*cosh(u)
    y=SQRT(2v)*sinh(u)

    then
    4*x^2=4*v/2*(cosh(u))^2
    y^2=2v*(sinh(u))^2

    and 4*x^2-y^2=2v*(cosh(u))^2-2v*(sinh(u))^2=2v*((cosh(u))^2-(sinh(u))^2)=2v
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  3. #3
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    Thank you so much!
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