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Math Help - equation of a plane touching a sphere

  1. #1
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    equation of a plane touching a sphere

    I need to find the equation for a plane that just touches a sphere (x - 4)^2 + (y + 1)^2 + (z - 3)^2 = 4 that is parallel to the xy plane

    In writing this I think I would just set x and y to zero and solve for z and therefore z = 5 would be the answer. Could someone please confirm this for me??

    So, if this were to be parallel to the zy plane then I would just solve for x with z and y at 0, Right? IN that case x would = 2


    THanks so much for all the assistance you folks have provided, it really helps. Frostking
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  2. #2
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    Hello, Frostking!

    This is easier than you think . . .


    Find the equation of a plane tangent to the sphere (x - 4)^2 + (y + 1)^2 + (z - 3)^2 \:=\: 4
    that is parallel to the xy-plane
    Try to visualize the graph . . .


    We have a sphere: center (4, -1, 3) and radius 2.

    A plane parallel to the xy-plane is "horizontal" . (z \,=\,\text{constant}).

    It would be tangent to the sphere at its "north pole" or "south pole."

    The north pole is (4, -1, 5); the south pole is (4,-1, 1).


    Hence, the tangent plane is either: . z = 5\:\text{ or }\:z = 1

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