Question
Form the differential equation of the family of curves represented by the equation (x – a)2 + 2 y2 = a2, a being the parameter.
Solution
The given equation is
...(1)
Differentiating both sides w.r.t.x , we get.
...(2)
and
...(3)
Putting the values of x - a, a from (2), (3) in (1), we get,
or
or
or
which is the required differential equation of the given family of curves.
...(1)Differentiating both sides w.r.t.x , we get.
...(2)and
...(3)Putting the values of x - a, a from (2), (3) in (1), we get,
or
or
or
which is the required differential equation of the given family of curves.
