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JEE Main2007MathematicsDifferential EquationsActual

The differential equation of all circles passing through the origin and having their centres on the x -axis is

Options

  1. Ax^2=y^2+x y d y d x
  2. Bx^2=y^2+3 x y d y d x
  3. Cy^2=x^2+2 x y d y d x
  4. Dy^2=x^2-2 x y d y d x

Correct answer

C. y^2=x^2+2 x y d y d x

Step-by-step solution

General equation of all such circles is x ^2+ y ^2+2 gx =0 . Differentiating, we get 2 x +2 y dy dx +2 g =0 Desired equation is aligned & x^2+y^2+ (-2 x-2 y d y d x ) x=0 & y^2=x^2+2 x y d y d x . aligned

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