Let C denote the family of circles in the second quadrant and touching the coordinate axes. Let (– a, a) be the coordinate of the centre of any member of this family.

Equation representing the family C is
(x + a)²+ (y – a)² = a²    ...(1)
or x² + y² + 2 ax – 2 a y + a² = 0    ...(2)
Differentiating equation (2) with respect to x, we get
                           
or              
or                             
Substituting the value of a in equation (1), we get
                                  
or        
or         
or        
which is the differential equation representing the given family of circles.