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AP EAMCET20225 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

If the normal drawn at a point P on the curve 3 y=6 x-5 x^3 passes through (0,0) , then the positive integral value of the abscissa of the point P is

Options

  1. A1
  2. B2 3
  3. C1 3
  4. D- 2 3

Correct answer

A. 1

Step-by-step solution

Given curve 3 y=6 x-5 x^3 d y d x =2-5 x^2 Slope of normal = -1 2-5 x^2 Equation of normal with slope -1 2-5 x^2 passing through origin (0,0) . (y-y₁ ) x-x₁ =m y-0 x-0 = -1 2-5 x^2 y x = -1 2-5 x^2 Since, (h, k) lies on normal k h = -1 2-5 h^2 k h = 1 5 h^2-2 ...(i) Since, (h, k) lies on curve 3 k=6 h-5 h^3 3 k=h (6-5 h^2 ) k h = 6-5 h^2 3 ...(ii) On solving Eqs. (i) and (ii), 1 5 h^2-2 = 6-5 h^2 3 aligned & 3= (6-5 h^2 ) (5 h^2-2 ) & 3=30 h^2-12-25 h^4+10 h^2 & 15=-25 h^4+40 h^2 & 5 h^4-8 h^2+3=0 aligned For simpl

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