The equation ax2 + ay2 + az2 + 2ux + 2vy + 2wz + d = 0, (a ≠ 0) represents a sphere if

1
u2 + v2 + w2 - d ≥ 0
2
u2 + v2 + w2 - ad ≥ 0
3
u2 + v2 + w2 - d ≤ 0
4
u2 + v2 + w2 - ad ≤ 0

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