Question

x^2+(y-b)^2 =1 ,b is an arbitrary

Answer 1

x=1

y=2

b=3 this is an arbitrary

Answer 2

A solution of an n-th order differential equation will consist of n arbitrary real constants. A family of curves with n arbitrary real constants will be represented by a differential equation of order n. ... So your required Differential equation representing the family of parabolas ...