#### Question

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

#### Solution

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.

Is there an error in this question or solution?

Solution Form the Differential Equation of the Family of Circles Touching the Y-axis at the Origin. Concept: Procedure to Form a Differential Equation that Will Represent a Given Family of Curves.