question_answer 1)

Form the differential equation of the family of parabolas having vertex at origin and axis along positive Y-axis. 

Answer:

Let (0, a) be the focus of a members of the given family of parabolas,                                 ?.. (1)             where a is any arbitrary constant.       Differentiate equation (1) w.r.t. x, we get                   Put the value of a in (1), we get                               which is the required differential equation.