The points on the sphere x+ y2 + z2 = 1 which are at the maximum and minumum distance from the point (3, 4, 12) are:

1
point A(4/13, 12/13, 4/13) at maximum distance and point B(-3/13, -4/13, -12/13) at minimum distance
2
point A(3/13, 4/13, 12/13) at minimum distance and point B(-3/13, -4/3, -12/13) maximum distance
3
point A(4/13, 12/13, 4/13) at minimum distance and point B(-3/13, -4/13, -12/13) at maximum distance
4
point A(12/13, -12/13, -4/13) at minimum distance and point B(-3/13, -4/13, -12/13) at maximum distance

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