The minimum distance of a point on the curve y = x 2 - 4 from the origin is

Question

The minimum distance of a point on the curve y = x 2 - 4 from the origin is, 15 2 units, 19 2 units, 15 2 units, 19 2 units

MARKS App · Accepted Answer

A variable point on the given parabola can be taken as α , α 2 - 4 Distance from origin D = α 2 + α 2 - 4 2 ⇒ D 2 = α 2 + α 4 + 16 - 8 α 2 = α 4 - 7 α 2 + 16 d D 2 d α = 4 α 3 - 14 α = 0 ⇒ 2 α 2 α 2 - 7 = 0 ⇒ α = 0 , 7 2 , - 7 2 ∴ D m i n 2 a t α 2 = 7 2 D m i n 2 = 49 4 - 49 2 + 16 = - 49 4 + 16 = 15 4 D m i n = 15 2

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