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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)

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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,...
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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 and A(0, 5is minimum at  or 

So, the correct answer is A.

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(A) (2√2, 4)
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I am expert in electrical engineering . I have b tech and m tech from nit warangal total experi 10 y

A
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