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

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

Now, the equation representing this family of circle is (x + a)² + (y – a)² = a² …… (i)

⇒ x² + y² + 2ax – 2ay + a² = 0 …… (ii)

Differentiating (ii) with respect to x we get,

Substituting this value of a in (i) we get,

The required differential equation is