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