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Let S be the set of all the natural numbers, for which the line 2 b y a x = + is a tangent to the curve 2 b y a x n n = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ at the point (a, b), ab ≠ 0. Then :

1. S = φ
2. n(S) = 1
3. S = {2k : k ∈ N }
4. S = N

Correct answer: S = N

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