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MHT CET202310 May 2023Evening ShiftMathematicsDifferential EquationsActual

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

Options

  1. Ay^2=x^2+x y d y ~d x
  2. Bx^2=y^2+2 x y d y ~d x
  3. Cy^2=x^2+2 x y d y ~d x
  4. Dx^2=y^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

The system of circles which passes through origin and whose centre lies on X -axis is x^2+y^2-2 b x=0... (i) Differentiating w.r.t x , we get 2 x+2 y d y ~d x =2 ~b ... (ii) Substituting (ii) in (i), we get aligned & x^2+y^2-2 x^2-2 x y d y ~d x =0 & y^2-x^2-2 x y d y ~d x =0 & y^2=x^2+2 x y d y ~d x aligned

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