The differential equation of the family of circles passing through the origin and having centre on X -axis is

• A

  $\left(y^2+x^2\right) d x-2 y d y=0$
• Correct answer
  B

  $\left(y^2-x^2\right) d x-2 x y d y=0$
• C

  $\left(y^2-x^2\right) d x+2 y d y=0$
• D

  $\left(y^2+x^2\right) d x+2 y d y=0$

Hence, the correct answer is option: 'B'.