R S Aggarwal Solutions for Exercise 3: EXERCISE

Form the differential equation of the family of all circles touching the $y$-axis at the origin.

From the differential equation of the family of circles having centres on $y$-axis and radius $2$ units.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes

Form the differential equation of the family of circles having centres on the $x$-axis and radius unity.

Form the differential equation of the family of circles passing through the fixed point $(a,0)$and $(-a,0)$, where $a$ is the fixed constant.

Form the differential equation of the family of parabolas having a vertex at the origin and axis along positive $y$-axis.

Form the differential equation of the family of an ellipse having foci on the $y$-axis and centres at the origin.

Form the differential equation of the family of hyperbolas having foci on the $x$-axis and centres at the origin.