Question

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

Answer 1

The centre of the circle touching the y-axis at origin lies on the x-axis.

Let (a, 0) be the centre of the circle.

Since it touches the y-axis at origin, its radius is a.

Now, the equation of the circle with centre (a, 0) and radius (a) is

This is the required differential equation.