The points on the curve y = x 2 which are closest to the point P 0,1 are

Question

The points on the curve y = x 2 which are closest to the point P 0,1 are, ± 2 , 2, ± 1 2 , 1 4, ± 1 2 , 1 2, ± 1 4 , 1 16

MARKS App · Accepted Answer

Let, the general point on the curve be Q α , α 2 ∴ P Q 2 = α 2 + α 2 - 1 2 = D (say) ⇒ D = α 4 - α 2 + 1 ⇒ d D d α = 4 α 3 - 2 α For P Q to be minimum, α 2 = 1 2 ⇒ α = ± 1 2 ∴ Q is ± 1 2 , 1 2

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