Question
Find the differential equation of all the circles in the first quadrant which touch the co-ordinate axes.
Solution
Let r be the radius of the circle whose centre is C and CM ⊥ x-axis, CN ⊥ y-axis.
∵ circle touches both the axes
∴ CM = CN = r
∴ C is (r, r)
∴ equation of circle is
(x - r)2 + (y – r)2 = r2 ...(1)
Differentiating both sides w.r.t.x,
or 
or 
Putting this value of r in (1), we get
or 
or 
or 
which is the required differential equation. 
