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MHT CET20242 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The co-ordinates of a point on the curve y=x x at which the normal is parallel to the line 2 x-2 y=3 are

Options

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

Correct answer

D. ( e ⁻²,-2 e ⁻² )

Step-by-step solution

aligned & y=x x & ~d y ~d x =1+ x ...(i) aligned Slope of the normal =- 1 ( ~d y ~d x ) = -1 1+ x Slope of the given line is 1 . Since the normal is parallel to the given line. aligned & -1 1+ x =1 & x=-2 & x= e ⁻² aligned From (i), y=-2 e ⁻² Co-ordinates of the point are ( e ⁻²,-2 e ⁻² ) .

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