Question

# The point on the curve x2=2y which is nearest to the point (0,5) is

A
(22,4)
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B
(22,0)
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C
(0,0)
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D
(2,2)
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E
(22,2)
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Solution

## The correct option is A (2√2,4)Point on a parabola can be taken to be (2at,at2). Here a=12So the point is (t,t22)Distance of this point from (0,5) will be √t2+(t22−5)2Lets minnimise D2 and we will get minimum distance automatically. First derivative of D2 is t3−8tPutting this to zero we get t=0 and t=±2√2Now let's do double derivative, it comes out to be 3t2−8.So, we can see that for t=0, distance is going to be maximum.So, distance is minimum from (2√2,4).

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