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 = x2 + 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 D2 is also minimum.

So, D2 =  


For minimum D2, we have 

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


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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