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Math Help - function for distance from a point outside a sphere to any point on its surface

  1. #1
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    function for distance from a point outside a sphere to any point on its surface

    Hi

    I have a point m outside a sphere. The sphere center is o and r is the radius of sphere. Distance from point m to o is l.
    If we draw a line from m to any point on the surface of sphere, this line has a length. Minimum length is l - r and maximum length would be l + r.
    I want the function for distance from m to any point on the surface of sphere. Also how to draw the graph of this function (all possible distances).

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    Last edited by mosibat; November 8th 2012 at 11:38 AM.
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  2. #2
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    Re: function for distance from a point outside a sphere to any point on its surface

    We can set up a coordinate system in which the sphere has center at the origin and the given point, m, is on the z-axis. The equation of the sphere in that coordinate system is x^2+ y^2+ z^2= r^2 and m is (0, 0, l). Given a point (x, y, z) on the sphere, above the xy-plane, then z= \sqrt{r^2- x^2- y^2} then the distance from m to that point is \sqrt{x^2+ y^2+ (l- \sqrt{r^2- x^2- y^2})^2}. If (x, y, z) is below the xy-plane, z= -\sqrt{r^2- x^2 y^2} then the distance is \sqrt{x^2+ y^2+ (l+ \sqrt{r^2- x^2- y^2})^2}.
    Thanks from mosibat
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    Re: function for distance from a point outside a sphere to any point on its surface

    Thanks. That was exactly what I was looking for.
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