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MHT CET202416 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The equation of the normal to the curve y=x x parallel to 2 x-2 y+3=0 is

Options

  1. Ax+y=3 e ⁻²
  2. Bx-y=3 e ⁻²
  3. Cx-y=3 e ^2
  4. Dx+y=3 e ^2

Correct answer

B. x-y=3 e ⁻²

Step-by-step solution

aligned & y=x x ...(i) & ~d y ~d x =1+ x 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 & y=-2 e ⁻² aligned ...[From (i)] Equation of the normal at ( e ⁻²,-2 e ⁻² ) is aligned & y+2 e ⁻²=1 (x- e ⁻² ) & y+2 e ⁻²=x- e ⁻² & x-y=3 e ⁻² aligned

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