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AP EAMCET202123 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

Find the coordinates of a point on the curve y=x^2-3 x+2 , at which the tangent drawn to this curve is perpendicular to the line y=x .

Options

  1. A(0,2)
  2. B(1,0)
  3. C(-1,6)
  4. D(2,-3)

Correct answer

B. (1,0)

Step-by-step solution

Given curve, y=x^2-3 x+2 On differentiating w.r.t. x , d y d x =2 x-3 Which represents the slope of tangent drawn to the curve. m₁=2 x-3 ...(i) Given line, y=x ...(ii) On comparing with y=m x+c Slope of line (ii), m₂=1 Tangent to the curve is perpendicular to line (ii). m₁ m₂=-1m₁ 1=-1 array cc & m₁=-1 & 2 x-3=-1 & 2 x=2 & x=1 array y=(1)^2-3 1+2y=0 Point of tangent drawn =(1,0)

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