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