The differential equation of the family of all circles of radius ' $a$ ' is

• A

  $y_1 y_2+\left(1+y_1^2\right)=a$
• Correct answer
  B

  $\left(1+y_1^2\right)^3=a^2 y_2^2$
• C

  $1+y_1^2=y_2^2+a^2$
• D

  $y_2^2+1=y_1^2+a^2$

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