Question
Determine the differential equation that will represent the family of all circles having centres on the x-axis and radius unity.
Solution
Let centre on x-axis be (a. 0). Also radius = 1
∴ the equation of the family of circles is
...(1)
Differentiating w.r.t x, we get,
or 
Putting this value of x - a in (1), we get,
which is required differential equation.
∴ the equation of the family of circles is
...(1)Differentiating w.r.t x, we get,
or Putting this value of x - a in (1), we get,
which is required differential equation.
