﻿ Find the point on the curve y = x2 which is closest to the point A(0, a).   : Kaysons Education

# Find The Point On The Curve y = x2 which Is Closest To The Point A(0, a).

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## Question

### Solution

Correct option is

Using the parametric representation, consider an arbitrary point P (tt2) on the curve.

Distance of P from A = PA

We have to find t so that this distance is minimum.

We will minimize PA2

Let         PA2 = (t) = t2 + (t2 – a)2

We have to consider two possibilities.

Case I: a = 1/2

In this case, t = 0 is the only value.

Hence the closest point corresponds to t = 0

⇒        (0, 0) is the closest point.

Case II: a > ½

Hence the distance is minimum for

So the closest points are

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