Find a constant c so that at any point of intersection of the two spheres $(x-c)^2+y^2+z^2=3$ and $x^2+(y-1)^2+z^2=1$ , the corresponding tangent planes are perpendicular to each other.
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you need to compute equation of tangent of both sphere and consider cases that perpendicular lines have negative reciprocal slopes – dato datuashvili Feb 08 '14 at 15:08
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this may help you http://math.stackexchange.com/questions/225614/tangent-plane-to-sphere – dato datuashvili Feb 08 '14 at 15:12