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MHT CET2008MathematicsApplication of Derivatives

The point of the curve y²=2(x-3) at which the normal is parallel to the line y-2 x+1=0 is

Options

  1. A(5,2)
  2. B(- 1 2 ,-2 )
  3. C(5,-2)
  4. D( 3 2 , 2 )

Correct answer

C. (5,-2)

Step-by-step solution

Given, y²=2(x-3) ...(i) On differentiating w.r.t. x , we get 2 y d y d x =2 d y d x = 1 y Slope of the normal = -1 (d y / d x) =-y Slope of the given line =2 y=-2 From Eq. (i), x=5 Required point is (5,-2) .

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