Question

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

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Answer 1

Answer:-

Refer the attachment

Answer 2

Answer:

Step-by-step explanation:

Application of derivatives and coordinate geometry:-

For a general parabola x^2=4ay in parametric form, coordinates are represented by:- (2at,at^2),where t is a parameter.

Here,a is 1/2

Using distance formula, distance is calculated between the general point and given point.

Differentiating the distance function wrt t,we substitute 0, and get three critical points.

Then doing double derivative test,we determine whether the critical point is a point of local maxima or local minima.

At t=2✓2, double derivative is positive, implying it is point of local minima.

Putting this value of t,we get minimum distance.