Question

Find the point on the curve y² = b which is at a minimum distance from the point (1,4).

Answer 1

The given equation of curve is y² = 2x and the given point is Q(1, 4).

Let P(x, y) be the point, which is at a minimum distance from point Q(1,4)

Now, distance between points P and Q is given by

On differentiating both sides w.r.t. y, we get

Hence, the point which is at a minimum distance from point (1, 4) is P(2, 2).