Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

Explanation

Equation of circle touching both axes is :
`(x-r)^(2)+(y-r)^(2)=r^(2)`…….`(1)`
Differentiate w.r.t.x,
`2(x-r)+2(y-r)(dy)/(dx)=0`
`implies x-r+y(dy)/(dx)-r(dy)/(dx)=0impliesr=(x+y(dy)/(dx))/(1+(dy)/(dx))`
put this value in equation `(1)`,
`{x-(x+y(dy)/(dx))/(1+(dy)/(dx))}^(2)+{y-(x+y(dy)/(dx))/(1+(dy)/(dx))}^(2)={(x+y(dy)/(dx))/(1+(dy)/(dx))}^(2)`
`=(x-y)^(2)((dy)/(dx))^(2)+(y-x)^(2)=(x+y(dy)/(dx))^(2)`
`implies (x-y)^(2){((dy)/(dx))^(2)+1}=(x+y(dy)/(dx))^(2)`