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Math Help - Plane tangent to a sphere

  1. #1
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    Plane tangent to a sphere

    If anyone could help me with this problem, it would be most appreciated.

    Find an equation for the plane tangent to the sphere x^2+y^2+z^2=81 at (1,4,8).

    I have tried finding the vector perpendicular to [1,4,8] but I end up with a+4b+8c=0 and can't figure out a way to find a, b, and c.

    Thanks.
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  2. #2
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    Quote Originally Posted by empireruler View Post
    Find an equation for the plane tangent to the sphere x^2+y^2+z^2=81 at (1,4,8).
    I have tried finding the vector perpendicular to [1,4,8] but I end up with a+4b+8c=0 and can't figure out a way to find a, b, and c.
    Don't stop! You are right there. Finish it off.
    The vector <1,4,8> is the normal.
    Use that normal and the point (1,4,8) to write the equation.
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  3. #3
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    Wait do you mean like x+4y+8z= 81... wouldn't that just give me the perpendicular plane... the one that shares the normal vector. Sorry if I missed the point you were getting at.
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    Quote Originally Posted by empireruler View Post
    Wait do you mean like x+4y+8z= 81... wouldn't that just give me the perpendicular plane... the one that shares the normal vector. Sorry if I missed the point you were getting at.
    What do you think a tangent plane means?
    Think about a tangent to a circle.
    It is perpendicular to a radial segment.
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  5. #5
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    wouldnt x+4y+8z = 81 be the plane that is parallel to the plane that is tangent to the sphere? Sorry I am not understanding
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  6. #6
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    Quote Originally Posted by empireruler View Post
    wouldnt x+4y+8z = 81 be the plane that is parallel to the plane that is tangent to the sphere? Sorry I am not understanding
    If it is parallel to the tangent plane and contains the point (1, 4, 8), which it does because 1+ 4(4)+ 8(8)= 1+ 16+ 64= 81, it is the tangent plane!
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