question_answer 30)

Form the differential equation of the family of circles touching Y-axis at origin.  

Answer:

Sol (a, 0) be the centre of member of the given family of circles touching Y-axis at origin.        = a2                                                  ?.. (1)       where a is any arbitrary constant.       Differentiate equation (1) w.r.t. x, we get       2x + 2yy? = 2a a = x + yy?       Put the value of a in (1), we get       x + y2 = 2x (x + yy?)                   which is the required differential equation.