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

To form: the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

The equation of the circle in second quadrant and touches the axes with center (-a, a) and radius a will be:

(x + a)² + (y – a)² = a²

where a is any arbitrary constant

Since there is one arbitrary constant, we need to differentiate it only once to get required differential equation

(x + a)² + (y – a)² = a² ……(i)

Differentiating both sides with respect to x:

Put this value of a in (i):

This is the required differential equation