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Manipal MET2011MathematicsApplication of Derivatives

The two curves x^3-3 x y^2+2=0 and 3 x^2 y-y^3=2

Options

  1. Acut at right angles
  2. Btouch each other
  3. Ccut at an angle / 3
  4. Dcut at an angle / 4

Correct answer

A. cut at right angles

Step-by-step solution

Given curves are x^3-3 x y^2+2=0 ..(i) and 3 x^2 y-y^3-2=0 ...(ii) On differentiating Eqs. (i) and (ii), with respect to x , we get ( d y d x ) C₁= x^2-y^2 2 x y aligned ( d y d x ) C₂ & = 2 x y x^2-y^2 ( d y d x )_ C₁ ( d y d x )_ C₂ & =-1 aligned

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