Question

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

(A) (B)

(C) (0, 0) (D) (2, 2)

Answer 1

The given curve is x² = 2y.

For each value of x, the position of the point will be

The distance d(x) between the points and (0, 5) is given by,

When,

When,

∴By second derivative test, d(x) is the minimum at.

When

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

The correct answer is A.