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JEE Main2004MathematicsDifferential EquationsActual

The differential equation for the family of curves x^2+y^2-2 a y=0 , where a is an arbitrary constant is

Options

  1. A2 (x^2-y^2 ) y^ =x y
  2. B2 (x^2+y^2 ) y^ =x y
  3. C(x^2-y^2 ) y^ =2 x y
  4. D(x^2+y^2 ) y^ =2 x y

Correct answer

C. (x^2-y^2 ) y^ =2 x y

Step-by-step solution

2 x+2 y y^ -2 a y^ =0a= x+y y^ y^ (eliminating a) (x^2-y^2 ) y^ =2 x y

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