Obtain the differential equation which corresponds to each of the following family of curves.
The ellipses with centress at the origin and having co-ordinate axes as axes

Obtain the differential equation which corresponds to each of the following family of curves. The circles which touch the Y - axis at the origin.

Obtain the differential equation which corresponds to each of the following family of curves. The parabolas having their foci at the origin and axis along the X - axis .

Obtain the differential equation which corresponds to each of the following family of curves. The rectangular hyperbolas which have the co-ordinate axes as asymptotes.

Obtain the differential equation which corresponds to each of the following family of curves. The parabolas each of which has a latus rectum 4a and whose axes are parallel to X-axis .

Obtain the differential equation of each of the following families of plane curves: circles having their centres on x-axis.

Obtain the differential equation of each of the following families of plane curves: all circles having centre at (1,2)

Obtain the differential equation of each of the following families of plane curves: circles with centre on y-axis.

Obtain the differential equation of each of the following families of plane curves: straight lines which pass through the origin.

Obtain the differential equation of each of the following families of plane curves: all circles which pass through the origin and whose centres lie on y-axis.

Obtain the differential equation of each of the following families of plane curves: all circles touching y-axis at origin.