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JEE Main202225 Jun 2022Evening ShiftMathematicsApplication of DerivativesActual

If the line y = 4 + k x , k > 0 , is the tangent to the parabola y = x - x 2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is

Options

  1. A3 2
  2. B26 9
  3. C5 2
  4. D23 6

Correct answer

C. 5 2

Step-by-step solution

Plotting the given data we have, Now by diagram, Slope of tangent at P = Slope of line AP d y d x α , α - α 2 = 1 − 2 α = α − α 2 − 4 α On solving we get α = - 2 ⇒ P - 2 , - 6 So, slope of P V = 5 2

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