The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2 x$ and eccentricity is $\sqrt{3}$ is

• A

  $(2 x-y) y_2+y_1^2-2 y_1=y_1^3+2$
• Correct answer
  B

  $(y-2 x) y_2+y_1^2+2 y_1=y_1^3+2$
• C

  $(y-2 x) y_2-y_1^2+2 y_1=y_1^3-2$
• D

  $(y+2 x) y_2+y_1^2+2 y_1=y_1^3-2$

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