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AP EAMCET202315 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The number of points on the cure y=2 t^2+3 t-5 and x=t^3-4 t^2-3 t such that the normals drawn at them on the curve are parallel to X - axis is

Options

  1. A1
  2. B4
  3. C3
  4. D2

Correct answer

B. 4

Step-by-step solution

d y d x = ( d y d t ) ( d x d t ) = 4 t+3 (3 t^2-8 t-3 ) Hence slope of normal =- 1 ( d y d x ) = (3 t^2-8 t-3 ) (4 t+3) Since slope of normal = Slope of x -axis aligned & 3 t^2-8 t-3 4 t+3 =0 & 3 t^2-8 t-3=0 & t=3 and t=- 1 3 aligned Hence required number of points =2

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