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AP EAMCET20226 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

The angle between the tangents drawn at (0,0) to the curves y^3-x^2 y+5 y-2 x=0 and x^4-x^3 y^2+5 x+2 y=0 is

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

D. 2

Step-by-step solution

aligned & y^3-x^2 y+5 y-2 x=0 & 3 y^2 d y d x -x^2 d y d x -2 x y+5 d y d x -2=0 & d y d x = 2 x y+2 3 y^2-x^2+5 & m₁= . d y d x |_ (0,0) = 2 5 aligned Now, x^4-x^3 y^2+5 x+2 y=0 aligned & 4 x^3-2 x^3 y d y d x -3 x^2 y^2+5+2 d y d x =0 & d y d x = 3 x^2 y^2-4 x^3-5 2-2 x^3 y & m₂= . d y d x |_ (0,0) = -5 2 & m₁ m₂= 2 5 -5 2 =-1 aligned The two lines are perpendicular i.e. angle between them is / 2 .

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