EXERCISE 10.3

. Find the differential equation of the family of (i) all non-vertical lines in a plane (ii) all non- horizontal lines in a plane. . Form the differential equation of all straight lines touching the circle x .

Find the differential equation of the family of circles passing through the origin and having their centres on the x -axis. . Find the differential equation of the family of all the parabolas with latus rectum a and whose axes are parallel to the x -axis. .

Find the differential equation of the family of parabolas with vertex at ( , and having axis along the y - axis. . Find the differential equations of the family of all the ellipses having foci on the y - axis and centre at the origin. .

Find the differential equation corresponding to the family of curves represented by the equation y