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KCET2016MathematicsApplication of Derivatives

The two curves ( x³-3 x y²+2=0 ) and ( 3 x² y-y³=2 )

Options

  1. ATouch each other
  2. BCut each other at right angle
  3. CCut at an angle ( 3 )
  4. DCut at an angle ( 4 )

Correct answer

B. Cut each other at right angle

Step-by-step solution

Given curves, ³-3 x y²+2=0 (1)3 x² y-y³=2 (2) Differentiating Eqs. (1) and (2) both the sides with respect to x , we get 3 x²-3 (y²+x (2 y y^ ) )=0 x²=y²+2 x y y^ y^ = x²-y² 2 x y =m₁( Let ) (3)3 (x² y^ +2 x y ) 3 y² y=0 x² y^ +2 x y-y² y^ =0 y^ = -2 x y x²-y² =m₂( Let ) (4) From Eqs. (3) and (4), we get m₁ m₂=-1 Hence, the two curves cut at an angle 2 i.e. right angle

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