A helicopter is flying along the curve y= x2+2.A soldier is placed at the point (3,2). Find the nearest distance between the soldier and the helicopter.(2010Sp)

Let the point (x, y) be the current position of helicopter along the curve (y = x^{2} + 2).

Given soldier is placed at the point (3,2).

Therefore, distance between helicopter and soldier = D

Now, we know that, if D is minimum then D^{2} is also minimum.

So, D^{2} =

For minimum D^{2}, we have

⇒ x = 1 as there are no real rots for the equation

Again,

Clearly, for x = 1, distance is minimum.

On putting value of x in the given curve , we get

y = (1)^{2} + 2 = 3

Therefore, point (1,3) is nearest to point (3,2)

Hence, minimum distance =

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