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Math Help - Equation for a surface

  1. #1
    aka
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    Equation for a surface

    Let L be the line y=7, x=5z. if we rotate L around the x-axis we get a surface whose equation is Ax^2+By^2+Cz^2=1
    Find A, B, C

    I got B=1/49 by setting x and z=0. Any hints on how to get A and C? I can show A=-25C by plugging in point (1,7,5) thinking I could get 2 equations with 2 unknowns thinking I could just use rref but all the second equation I've been able to get just says A=C=0 which is incorrect.
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  2. #2
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    The point (0,0,7) also lies on the surface giving C=1/49. You can now substitute this in to get A.
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  3. #3
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    Quote Originally Posted by aka View Post
    Let L be the line y=7, x=5z. if we rotate L around the x-axis we get a surface whose equation is Ax^2+By^2+Cz^2=1
    Find A, B, C

    I got B=1/49 by setting x and z=0. Any hints on how to get A and C? I can show A=-25C by plugging in point (1,7,5)
    No, (1, 7, 5) is not on the surface. Since "x= 5z" you want (5, 7, 1).

    thinking I could get 2 equations with 2 unknowns thinking I could just use rref but all the second equation I've been able to get just says A=C=0 which is incorrect.
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