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Math Help - Finding all points on the surface parallel to a plane

  1. #1
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    Finding all points on the surface parallel to a plane

    "Consider the surface given by 4x^2-y^2+5z^2-10z=55.

    a) Find all points on the surface at which the tangent plane is parallel to the plane 8x+y+15z=1.
    b) Pick one of these points and give the equation of the tangent plane to the surface at that point."

    My work so far:

    I'm stuck on this one. Part B is easy enough once you figure out part A, but I'm not sure what to do after a certain point.

    g(x,y,z)= 8x, -2y, 10z-10

    So what I'm looking for is a value of k such that 8x, -2y, 10z-10 = k (8,1,15).

    But I don't know how to find k. Any help would be appreciated.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    The point (x,y,z)=(k,-k/2,(10+15k)/10) with k\neq 0 must satisfy the equation of the surface.
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