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Math Help - Find equation for tangent plane

  1. #1
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    Find equation for tangent plane

    Find the equation for the tangent plane to the surface x^2+3xyz+y^2=-5z^2 at the point (1,1,1).

    I found the answer to be x+y+3z=5 but my solution manual says -5x-5y+7z=-3.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by joepinsley View Post
    Find the equation for the tangent plane to the surface x^2+3xyz+y^2=-5z^2 at the point (1,1,1).

    I found the answer to be x+y+3z=5 but my solution manual says -5x-5y+7z=-3.
    It should be x^2+3xyz+y^2=5z^2 (no negative sign before 5z^2). Then

    f(x,y,z)=x^2+3xyz+y^2-5z^2=0

    \nabla f = \langle 2x+3yz,3xz+2y,3xy-10z\rangle

    Plug in (1,1,1) to get \langle 5,5,-7\rangle

    So it's 5(x-1)+5(y-1)-7(z-1)=0\implies 5x+5y-7z=3 (or -5x-5y+7z=-3 if you prefer).
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