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The point on the curve x2 = 2y which is nearest to the point (0, 5) is
(A) (B)
(C) (0, 0) (D) (2, 2)
The given curve is x2 = 2y.
For each value of x, the position of the point will be
Let P and A(0, 5) are the given points.
Now distance between the points P and A is given by,
Let us denote PA2 by Z. Then,
Z =
Differentiating both sides with respect to y, we get
For maxima or minima, we have
Now,
⇒ = 2×4
⇒
or
So, Z is minimum at or
Or, PA2 is minimum at or
Or, PA is minimum at or
So, distance between the points P and A(0, 5) is minimum at or
So, the correct answer is A.
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